Why do Risk Premia exist?

When I entered this industry several years ago, I blew my first real interview because I didn’t understand the concept of a risk premium. Ironically, I later heard through the grapevine that I performed well during interview, but I was struggling with my unwillingness to invest as my analysis suggested that I should, and I later wrote an email explaining my discomfort involving stuff from my old probability studies in physics. It apparently was this follow-up letter that struck the interviewer as strange, and he decided to look elsewhere. In retrospect, what was missing from the analysis was a better understanding of risk premiums.

The interviewer asked me how much I should be willing to pay today for a contract where he would pay me $100 in six months if the temperature were above the historical median for that day. The expected value of that bet is fairly simple: $50, and I knew enough from economics to know that the $50 needed to be discounted to the present to come up with the contract’s present value. Assuming that treasuries were yielding 4%, the contract would seem to be worth $49 today.

Although I felt comfortable with the analysis, I struggled with the fact that, were I pressed in real life, I would not have been willing to pay $49 for that contract. I was unemployed at the time, and my savings were especially needed, and so I would not have been willing to put that money at risk. That instinct turned out to be the right one, but at the time I did not understand why.

To make the contract attractive, the price would need to be less than $49. If the contract had simply been to pay me $50 (and I was certain it would be honored, and I didn’t need the money before then, and there were no other attractive investment), then $49 would have been more or less the right price. But the interviewer wasn’t going to pay $50; he was going to pay $100, or possibly $0. In other words, there was risk. Risk made me uneasy, even more so, given my conditions at the time. That uneasiness deserves compensation, and it turns out to be appropriate to compensate.

Why is there a risk premium?

A substantial part of financial analysis is about estimating the right premium to compensate an investor for taking on investment risk. To figure a risk premium correctly, it helps to understand why there should be one in the first place.

It turns out that a risk premium is a natural outcome of the economic principle of diminishing utility. Without the jargon, risk premia come from the fact that, although winning $200 is twice as much as just winning $100, and definitely better, it is less than twice as satisfying.

A utility function tells us how “satisfying” it is to have a particular quantity of money or combination of goods. It converts an observable quantity like “dollars in the bank” to the “degree of satisfaction” those dollars confer. Utilities are notoriously difficult to work with in practice, because they cannot be quantified directly, and one person’s utility function, even if it could be observed, may not be comparable to another person’s function (this causes difficulties in welfare economics because it implies that there is no aggregable social welfare function for public policy makers to maximize).

There are two things we know do about utility functions: 1) having more wealth should be preferable to having less (at extreme wealth levels even this might not be true, but that is a subject for a different post), and 2) as one acquires more, additional wealth provides less additional satisfaction, an effect called “decreasing marginal utility.”

There is a rational reason to expect decreasing marginal utility: if I give you $10,000, you are likely to be happy and use it for the things that matter most on your list of wants and needs. If I hand you a second $10,000, you are likely to be even happier, but the things you use it for will be less essential to you than with the first $10,000 you gained, or else you would have attended to them with the first $10k, rather than wait for the second (which presumably you did not know was coming).

The mathematical implication of an increasing utility function with decreasing marginal utility is that a graph of utility vs. wealth should look roughly like figure 1, always growing with wealth, but flattening out and growing more slowly as wealth increases.

[ Click for Figure 1 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig1.jpg”>

The curvature of the utility curve is important, because it is ultimately the reason for the risk premium.

Let’s assume now that we are about to enter a risky investment. To keep it simple, we will have one of two outcomes, with equal likelihood. Either we will get a high payoff, labeled as H on Figure 2, or we will get a low payoff, labeled L on the same figure. Since both payoffs have an equal likelihood of occurring, the expected payoff, E(x), is simply the average of the two outcome, and sits exactly between the the positive and negative outcomes (shown as (x+∂) and (x-∂) on the figure).

[ Click for Figure 2 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig2.jpg”>

Now look at the utilities for this scenario. Just as we can compute expected wealth as the average of H and L’s wealth, we can also compute expected utility by averaging the utility expected at H and L. This utility is also exactly halfway between H’s and L’s utility, and is shown by point A on Figure 2. But point A (the expected utility with risk) delivers less utility (i.e. satisfaction) than the one would get if we were just guaranteed E(x). The fact that we are either going to have (x+∂) or (x-∂) at the end of the investment means that our investment’s expected utility E(U) is less than the utility of the expected outcome U( E[x] ), simply because there is risk involved.

In other words, the expected utility of a risky bet is less than the utility of the bet’s expected value. Mathematically,

        E(U) < U( E(x) )

[ Click for Figure 3 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig3.jpg”>

Figure 3 goes a step further, and shows that this risky bet has the same expected utility as another wealth outcome, xc, sometimes called the “certainty equivalent” wealth. The certainty equivalent wealth (point C on Figure 3) represents the level of wealth that - if guaranteed - provides the same degree as satisfaction as the expected utility of the risky option. Importantly, because of the way the utility function curves, the certainty equivalent wealth, xc, is always less than the expected wealth, E(x).

Since an investor is really trying to maximize expected utility, not expected wealth, the value of the risky bet to that investor is actually xc, the certainty equivalent, and not E(x), the expected value, because both the certainty equivalent and the risky investment produce the same expected utility.

As a result, it is xc, the certainty equivalent, not E(x), that should be discounted to the present to account for the time value of money, because PV(xc) is the value that, if invested today without any risk, will produce the same expected satisfaction to the investor.

And how do we get from E(x), which we can hope to compute from expected outcomes, to xc, the non-risky equivalent? We discount E(x) by a risk premium to estimate xc.

How much discounting is necessary? If one could observe the true utility curve, and therefore calculate xc, the risk premium would be:

        Risk Premium = [ E(x) / xc ] - 1

Mathematically, xc is is the inverse utility function, applied to the investment’s expected utility xc = U-1( E(U) ). On first blush, it would look like the inverse utility function simply “undoes” the utility calculation based on the investment’s performance, but if we remember that E(U) < U( E(x) ), we can see again that xc < E(x).

Getting at the risk premium

Obviously, as nice as it would be to use mathematics to calculate the true risk premium, the problem is that we can’t really observe utility functions in practice, and therefore there is no formula that can truly tell us what risk premium we should really use for our own investments. As investment analysts, however, we might be able to sense our own utility functions, even if it is difficult to map the functions of others.

For example, we can ask ourselves how much we would feel comfortable paying for an investment if we were to receive the investment result by day’s end, rather than at the end of the investment horizon. Doing this focuses our analysis solely on the risk aspect of the investment, rather than confounding the risk with the time aspect. Although an answer by this method is admittedly determined subjectively, it does give us a sense of the appropriate discount to use for the risk premium. We should not be surprised if our “comfortable price” turns out to be less than the investment’s expected value; indeed, we should expect it. How much less gives us the risk premium.

As mentioned, the advantage of this method is that it separates the time component of an investment’s discount factor from its risk component. Normally, when risk factors are estimated, they are “added on top of” the discount factor for time value (a.k.a the risk-free rate). This encourages investment analysts to project the risks further into the future, making risks seem more abstract than they really are. By thinking in terms of an investment result that, while unknown, will be known later today, we can focus our minds specifically on the risk, rather than conflating it with the discount for time. The suggested mechanism is:

1) Evaluate risks as quantitatively as possible, and determine expected value E(x).

2) Determine a risk discount, based on the price, P, you would be comfortable paying for the investment, assuming that the result becomes known and delivered later that same day. Then the risk premium, RP = E(x) / P.

3) Discount P to the present, using the risk-free rate (RFR) as the discount factor for the time value of money.

Working backwards, we see that the discount rate is then constructed as: Discount Rate = RFR + RP .

Future posts on risk premia

This analysis of the origin of risk premia has some additional implications that I want to cover in a future post. Most importantly, it suggests that risk premia may change not simply a result of asset volatility (though it responds to that too), but also can be the result of changing utility curves. The implications of this for investment strategy are many, and I will return to them in a later post.

Why do Risk Premia exist?

When I entered this industry several years ago, I blew my first real interview because I didn’t understand the concept of a risk premium. Ironically, I later heard through the grapevine that I performed well during interview, but I was struggling with my unwillingness to invest as my analysis suggested that I should, and I later wrote an email explaining my discomfort involving stuff from my old probability studies in physics. It apparently was this follow-up letter that struck the interviewer as strange, and he decided to look elsewhere. In retrospect, what was missing from the analysis was a better understanding of risk premiums.

The interviewer asked me how much I should be willing to pay today for a contract where he would pay me $100 in six months if the temperature were above the historical median for that day. The expected value of that bet is fairly simple: $50, and I knew enough from economics to know that the $50 needed to be discounted to the present to come up with the contract’s present value. Assuming that treasuries were yielding 4%, the contract would seem to be worth $49 today.

Although I felt comfortable with the analysis, I struggled with the fact that, were I pressed in real life, I would not have been willing to pay $49 for that contract. I was unemployed at the time, and my savings were especially needed, and so I would not have been willing to put that money at risk. That instinct turned out to be the right one, but at the time I did not understand why.

To make the contract attractive, the price would need to be less than $49. If the contract had simply been to pay me $50 (and I was certain it would be honored, and I didn’t need the money before then, and there were no other attractive investment), then $49 would have been more or less the right price. But the interviewer wasn’t going to pay $50; he was going to pay $100, or possibly $0. In other words, there was risk. Risk made me uneasy, even more so, given my conditions at the time. That uneasiness deserves compensation, and it turns out to be appropriate to compensate.

Why is there a risk premium?

A substantial part of financial analysis is about estimating the right premium to compensate an investor for taking on investment risk. To figure a risk premium correctly, it helps to understand why there should be one in the first place.

It turns out that a risk premium is a natural outcome of the economic principle of diminishing utility. Without the jargon, risk premia come from the fact that, although winning $200 is twice as much as just winning $100, and definitely better, it is less than twice as satisfying.

A utility function tells us how “satisfying” it is to have a particular quantity of money or combination of goods. It converts an observable quantity like “dollars in the bank” to the “degree of satisfaction” those dollars confer. Utilities are notoriously difficult to work with in practice, because they cannot be quantified directly, and one person’s utility function, even if it could be observed, may not be comparable to another person’s function (this causes difficulties in welfare economics because it implies that there is no aggregable social welfare function for public policy makers to maximize).

There are two things we know do about utility functions: 1) having more wealth should be preferable to having less (at extreme wealth levels even this might not be true, but that is a subject for a different post), and 2) as one acquires more, additional wealth provides less additional satisfaction, an effect called “decreasing marginal utility.”

There is a rational reason to expect decreasing marginal utility: if I give you $10,000, you are likely to be happy and use it for the things that matter most on your list of wants and needs. If I hand you a second $10,000, you are likely to be even happier, but the things you use it for will be less essential to you than with the first $10,000 you gained, or else you would have attended to them with the first $10k, rather than wait for the second (which presumably you did not know was coming).

The mathematical implication of an increasing utility function with decreasing marginal utility is that a graph of utility vs. wealth should look roughly like figure 1, always growing with wealth, but flattening out and growing more slowly as wealth increases.

[ Click for Figure 1 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig1.jpg”>

The curvature of the utility curve is important, because it is ultimately the reason for the risk premium.

Let’s assume now that we are about to enter a risky investment. To keep it simple, we will have one of two outcomes, with equal likelihood. Either we will get a high payoff, labeled as H on Figure 2, or we will get a low payoff, labeled L on the same figure. Since both payoffs have an equal likelihood of occurring, the expected payoff, E(x), is simply the average of the two outcome, and sits exactly between the the positive and negative outcomes (shown as (x+∂) and (x-∂) on the figure).

[ Click for Figure 2 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig2.jpg”>

Now look at the utilities for this scenario. Just as we can compute expected wealth as the average of H and L’s wealth, we can also compute expected utility by averaging the utility expected at H and L. This utility is also exactly halfway between H’s and L’s utility, and is shown by point A on Figure 2. But point A (the expected utility with risk) delivers less utility (i.e. satisfaction) than the one would get if we were just guaranteed E(x). The fact that we are either going to have (x+∂) or (x-∂) at the end of the investment means that our investment’s expected utility E(U) is less than the utility of the expected outcome U( E[x] ), simply because there is risk involved.

In other words, the expected utility of a risky bet is less than the utility of the bet’s expected value. Mathematically,

        E(U) < U( E(x) )

[ Click for Figure 3 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig3.jpg”>

Figure 3 goes a step further, and shows that this risky bet has the same expected utility as another wealth outcome, xc, sometimes called the “certainty equivalent” wealth. The certainty equivalent wealth (point C on Figure 3) represents the level of wealth that - if guaranteed - provides the same degree as satisfaction as the expected utility of the risky option. Importantly, because of the way the utility function curves, the certainty equivalent wealth, xc, is always less than the expected wealth, E(x).

Since an investor is really trying to maximize expected utility, not expected wealth, the value of the risky bet to that investor is actually xc, the certainty equivalent, and not E(x), the expected value, because both the certainty equivalent and the risky investment produce the same expected utility.

As a result, it is xc, the certainty equivalent, not E(x), that should be discounted to the present to account for the time value of money, because PV(xc) is the value that, if invested today without any risk, will produce the same expected satisfaction to the investor.

And how do we get from E(x), which we can hope to compute from expected outcomes, to xc, the non-risky equivalent? We discount E(x) by a risk premium to estimate xc.

How much discounting is necessary? If one could observe the true utility curve, and therefore calculate xc, the risk premium would be:

        Risk Premium = [ E(x) / xc ] - 1

Mathematically, xc is is the inverse utility function, applied to the investment’s expected utility xc = U-1( E(U) ). On first blush, it would look like the inverse utility function simply “undoes” the utility calculation based on the investment’s performance, but if we remember that E(U) < U( E(x) ), we can see again that xc < E(x).

Getting at the risk premium

Obviously, as nice as it would be to use mathematics to calculate the true risk premium, the problem is that we can’t really observe utility functions in practice, and therefore there is no formula that can truly tell us what risk premium we should really use for our own investments. As investment analysts, however, we might be able to sense our own utility functions, even if it is difficult to map the functions of others.

For example, we can ask ourselves how much we would feel comfortable paying for an investment if we were to receive the investment result by day’s end, rather than at the end of the investment horizon. Doing this focuses our analysis solely on the risk aspect of the investment, rather than confounding the risk with the time aspect. Although an answer by this method is admittedly determined subjectively, it does give us a sense of the appropriate discount to use for the risk premium. We should not be surprised if our “comfortable price” turns out to be less than the investment’s expected value; indeed, we should expect it. How much less gives us the risk premium.

As mentioned, the advantage of this method is that it separates the time component of an investment’s discount factor from its risk component. Normally, when risk factors are estimated, they are “added on top of” the discount factor for time value (a.k.a the risk-free rate). This encourages investment analysts to project the risks further into the future, making risks seem more abstract than they really are. By thinking in terms of an investment result that, while unknown, will be known later today, we can focus our minds specifically on the risk, rather than conflating it with the discount for time. The suggested mechanism is:

1) Evaluate risks as quantitatively as possible, and determine expected value E(x).

2) Determine a risk discount, based on the price, P, you would be comfortable paying for the investment, assuming that the result becomes known and delivered later that same day. Then the risk premium, RP = E(x) / P.

3) Discount P to the present, using the risk-free rate (RFR) as the discount factor for the time value of money.

Working backwards, we see that the discount rate is then constructed as: Discount Rate = RFR + RP .

Future posts on risk premia

This analysis of the origin of risk premia has some additional implications that I want to cover in a future post. Most importantly, it suggests that risk premia may change not simply a result of asset volatility (though it responds to that too), but also can be the result of changing utility curves. The implications of this for investment strategy are many, and I will return to them in a later post.

Why do Risk Premia exist?

When I entered this industry several years ago, I blew my first real interview because I didn’t understand the concept of a risk premium. Ironically, I later heard through the grapevine that I performed well during interview, but I was struggling with my unwillingness to invest as my analysis suggested that I should, and I later wrote an email explaining my discomfort involving stuff from my old probability studies in physics. It apparently was this follow-up letter that struck the interviewer as strange, and he decided to look elsewhere. In retrospect, what was missing from the analysis was a better understanding of risk premiums.

The interviewer asked me how much I should be willing to pay today for a contract where he would pay me $100 in six months if the temperature were above the historical median for that day. The expected value of that bet is fairly simple: $50, and I knew enough from economics to know that the $50 needed to be discounted to the present to come up with the contract’s present value. Assuming that treasuries were yielding 4%, the contract would seem to be worth $49 today.

Although I felt comfortable with the analysis, I struggled with the fact that, were I pressed in real life, I would not have been willing to pay $49 for that contract. I was unemployed at the time, and my savings were especially needed, and so I would not have been willing to put that money at risk. That instinct turned out to be the right one, but at the time I did not understand why.

To make the contract attractive, the price would need to be less than $49. If the contract had simply been to pay me $50 (and I was certain it would be honored, and I didn’t need the money before then, and there were no other attractive investment), then $49 would have been more or less the right price. But the interviewer wasn’t going to pay $50; he was going to pay $100, or possibly $0. In other words, there was risk. Risk made me uneasy, even more so, given my conditions at the time. That uneasiness deserves compensation, and it turns out to be appropriate to compensate.

Why is there a risk premium?

A substantial part of financial analysis is about estimating the right premium to compensate an investor for taking on investment risk. To figure a risk premium correctly, it helps to understand why there should be one in the first place.

It turns out that a risk premium is a natural outcome of the economic principle of diminishing utility. Without the jargon, risk premia come from the fact that, although winning $200 is twice as much as just winning $100, and definitely better, it is less than twice as satisfying.

A utility function tells us how “satisfying” it is to have a particular quantity of money or combination of goods. It converts an observable quantity like “dollars in the bank” to the “degree of satisfaction” those dollars confer. Utilities are notoriously difficult to work with in practice, because they cannot be quantified directly, and one person’s utility function, even if it could be observed, may not be comparable to another person’s function (this causes difficulties in welfare economics because it implies that there is no aggregable social welfare function for public policy makers to maximize).

There are two things we know do about utility functions: 1) having more wealth should be preferable to having less (at extreme wealth levels even this might not be true, but that is a subject for a different post), and 2) as one acquires more, additional wealth provides less additional satisfaction, an effect called “decreasing marginal utility.”

There is a rational reason to expect decreasing marginal utility: if I give you $10,000, you are likely to be happy and use it for the things that matter most on your list of wants and needs. If I hand you a second $10,000, you are likely to be even happier, but the things you use it for will be less essential to you than with the first $10,000 you gained, or else you would have attended to them with the first $10k, rather than wait for the second (which presumably you did not know was coming).

The mathematical implication of an increasing utility function with decreasing marginal utility is that a graph of utility vs. wealth should look roughly like figure 1, always growing with wealth, but flattening out and growing more slowly as wealth increases.

[ Click for Figure 1 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig1.jpg”>

The curvature of the utility curve is important, because it is ultimately the reason for the risk premium.

Let’s assume now that we are about to enter a risky investment. To keep it simple, we will have one of two outcomes, with equal likelihood. Either we will get a high payoff, labeled as H on Figure 2, or we will get a low payoff, labeled L on the same figure. Since both payoffs have an equal likelihood of occurring, the expected payoff, E(x), is simply the average of the two outcome, and sits exactly between the the positive and negative outcomes (shown as (x+∂) and (x-∂) on the figure).

[ Click for Figure 2 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig2.jpg”>

Now look at the utilities for this scenario. Just as we can compute expected wealth as the average of H and L’s wealth, we can also compute expected utility by averaging the utility expected at H and L. This utility is also exactly halfway between H’s and L’s utility, and is shown by point A on Figure 2. But point A (the expected utility with risk) delivers less utility (i.e. satisfaction) than the one would get if we were just guaranteed E(x). The fact that we are either going to have (x+∂) or (x-∂) at the end of the investment means that our investment’s expected utility E(U) is less than the utility of the expected outcome U( E[x] ), simply because there is risk involved.

In other words, the expected utility of a risky bet is less than the utility of the bet’s expected value. Mathematically,

        E(U) < U( E(x) )

[ Click for Figure 3 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig3.jpg”>

Figure 3 goes a step further, and shows that this risky bet has the same expected utility as another wealth outcome, xc, sometimes called the “certainty equivalent” wealth. The certainty equivalent wealth (point C on Figure 3) represents the level of wealth that - if guaranteed - provides the same degree as satisfaction as the expected utility of the risky option. Importantly, because of the way the utility function curves, the certainty equivalent wealth, xc, is always less than the expected wealth, E(x).

Since an investor is really trying to maximize expected utility, not expected wealth, the value of the risky bet to that investor is actually xc, the certainty equivalent, and not E(x), the expected value, because both the certainty equivalent and the risky investment produce the same expected utility.

As a result, it is xc, the certainty equivalent, not E(x), that should be discounted to the present to account for the time value of money, because PV(xc) is the value that, if invested today without any risk, will produce the same expected satisfaction to the investor.

And how do we get from E(x), which we can hope to compute from expected outcomes, to xc, the non-risky equivalent? We discount E(x) by a risk premium to estimate xc.

How much discounting is necessary? If one could observe the true utility curve, and therefore calculate xc, the risk premium would be:

        Risk Premium = [ E(x) / xc ] - 1

Mathematically, xc is is the inverse utility function, applied to the investment’s expected utility xc = U-1( E(U) ). On first blush, it would look like the inverse utility function simply “undoes” the utility calculation based on the investment’s performance, but if we remember that E(U) < U( E(x) ), we can see again that xc < E(x).

Getting at the risk premium

Obviously, as nice as it would be to use mathematics to calculate the true risk premium, the problem is that we can’t really observe utility functions in practice, and therefore there is no formula that can truly tell us what risk premium we should really use for our own investments. As investment analysts, however, we might be able to sense our own utility functions, even if it is difficult to map the functions of others.

For example, we can ask ourselves how much we would feel comfortable paying for an investment if we were to receive the investment result by day’s end, rather than at the end of the investment horizon. Doing this focuses our analysis solely on the risk aspect of the investment, rather than confounding the risk with the time aspect. Although an answer by this method is admittedly determined subjectively, it does give us a sense of the appropriate discount to use for the risk premium. We should not be surprised if our “comfortable price” turns out to be less than the investment’s expected value; indeed, we should expect it. How much less gives us the risk premium.

As mentioned, the advantage of this method is that it separates the time component of an investment’s discount factor from its risk component. Normally, when risk factors are estimated, they are “added on top of” the discount factor for time value (a.k.a the risk-free rate). This encourages investment analysts to project the risks further into the future, making risks seem more abstract than they really are. By thinking in terms of an investment result that, while unknown, will be known later today, we can focus our minds specifically on the risk, rather than conflating it with the discount for time. The suggested mechanism is:

1) Evaluate risks as quantitatively as possible, and determine expected value E(x).

2) Determine a risk discount, based on the price, P, you would be comfortable paying for the investment, assuming that the result becomes known and delivered later that same day. Then the risk premium, RP = E(x) / P.

3) Discount P to the present, using the risk-free rate (RFR) as the discount factor for the time value of money.

Working backwards, we see that the discount rate is then constructed as: Discount Rate = RFR + RP .

Future posts on risk premia

This analysis of the origin of risk premia has some additional implications that I want to cover in a future post. Most importantly, it suggests that risk premia may change not simply a result of asset volatility (though it responds to that too), but also can be the result of changing utility curves. The implications of this for investment strategy are many, and I will return to them in a later post.

Why do Risk Premia exist?

When I entered this industry several years ago, I blew my first real interview because I didn’t understand the concept of a risk premium. Ironically, I later heard through the grapevine that I performed well during interview, but I was struggling with my unwillingness to invest as my analysis suggested that I should, and I later wrote an email explaining my discomfort involving stuff from my old probability studies in physics. It apparently was this follow-up letter that struck the interviewer as strange, and he decided to look elsewhere. In retrospect, what was missing from the analysis was a better understanding of risk premiums.

The interviewer asked me how much I should be willing to pay today for a contract where he would pay me $100 in six months if the temperature were above the historical median for that day. The expected value of that bet is fairly simple: $50, and I knew enough from economics to know that the $50 needed to be discounted to the present to come up with the contract’s present value. Assuming that treasuries were yielding 4%, the contract would seem to be worth $49 today.

Although I felt comfortable with the analysis, I struggled with the fact that, were I pressed in real life, I would not have been willing to pay $49 for that contract. I was unemployed at the time, and my savings were especially needed, and so I would not have been willing to put that money at risk. That instinct turned out to be the right one, but at the time I did not understand why.

To make the contract attractive, the price would need to be less than $49. If the contract had simply been to pay me $50 (and I was certain it would be honored, and I didn’t need the money before then, and there were no other attractive investment), then $49 would have been more or less the right price. But the interviewer wasn’t going to pay $50; he was going to pay $100, or possibly $0. In other words, there was risk. Risk made me uneasy, even more so, given my conditions at the time. That uneasiness deserves compensation, and it turns out to be appropriate to compensate.

Why is there a risk premium?

A substantial part of financial analysis is about estimating the right premium to compensate an investor for taking on investment risk. To figure a risk premium correctly, it helps to understand why there should be one in the first place.

It turns out that a risk premium is a natural outcome of the economic principle of diminishing utility. Without the jargon, risk premia come from the fact that, although winning $200 is twice as much as just winning $100, and definitely better, it is less than twice as satisfying.

A utility function tells us how “satisfying” it is to have a particular quantity of money or combination of goods. It converts an observable quantity like “dollars in the bank” to the “degree of satisfaction” those dollars confer. Utilities are notoriously difficult to work with in practice, because they cannot be quantified directly, and one person’s utility function, even if it could be observed, may not be comparable to another person’s function (this causes difficulties in welfare economics because it implies that there is no aggregable social welfare function for public policy makers to maximize).

There are two things we know do about utility functions: 1) having more wealth should be preferable to having less (at extreme wealth levels even this might not be true, but that is a subject for a different post), and 2) as one acquires more, additional wealth provides less additional satisfaction, an effect called “decreasing marginal utility.”

There is a rational reason to expect decreasing marginal utility: if I give you $10,000, you are likely to be happy and use it for the things that matter most on your list of wants and needs. If I hand you a second $10,000, you are likely to be even happier, but the things you use it for will be less essential to you than with the first $10,000 you gained, or else you would have attended to them with the first $10k, rather than wait for the second (which presumably you did not know was coming).

The mathematical implication of an increasing utility function with decreasing marginal utility is that a graph of utility vs. wealth should look roughly like figure 1, always growing with wealth, but flattening out and growing more slowly as wealth increases.

[ Click for Figure 1 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig1.jpg”>

The curvature of the utility curve is important, because it is ultimately the reason for the risk premium.

Let’s assume now that we are about to enter a risky investment. To keep it simple, we will have one of two outcomes, with equal likelihood. Either we will get a high payoff, labeled as H on Figure 2, or we will get a low payoff, labeled L on the same figure. Since both payoffs have an equal likelihood of occurring, the expected payoff, E(x), is simply the average of the two outcome, and sits exactly between the the positive and negative outcomes (shown as (x+∂) and (x-∂) on the figure).

[ Click for Figure 2 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig2.jpg”>

Now look at the utilities for this scenario. Just as we can compute expected wealth as the average of H and L’s wealth, we can also compute expected utility by averaging the utility expected at H and L. This utility is also exactly halfway between H’s and L’s utility, and is shown by point A on Figure 2. But point A (the expected utility with risk) delivers less utility (i.e. satisfaction) than the one would get if we were just guaranteed E(x). The fact that we are either going to have (x+∂) or (x-∂) at the end of the investment means that our investment’s expected utility E(U) is less than the utility of the expected outcome U( E[x] ), simply because there is risk involved.

In other words, the expected utility of a risky bet is less than the utility of the bet’s expected value. Mathematically,

        E(U) < U( E(x) )

[ Click for Figure 3 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig3.jpg”>

Figure 3 goes a step further, and shows that this risky bet has the same expected utility as another wealth outcome, xc, sometimes called the “certainty equivalent” wealth. The certainty equivalent wealth (point C on Figure 3) represents the level of wealth that - if guaranteed - provides the same degree as satisfaction as the expected utility of the risky option. Importantly, because of the way the utility function curves, the certainty equivalent wealth, xc, is always less than the expected wealth, E(x).

Since an investor is really trying to maximize expected utility, not expected wealth, the value of the risky bet to that investor is actually xc, the certainty equivalent, and not E(x), the expected value, because both the certainty equivalent and the risky investment produce the same expected utility.

As a result, it is xc, the certainty equivalent, not E(x), that should be discounted to the present to account for the time value of money, because PV(xc) is the value that, if invested today without any risk, will produce the same expected satisfaction to the investor.

And how do we get from E(x), which we can hope to compute from expected outcomes, to xc, the non-risky equivalent? We discount E(x) by a risk premium to estimate xc.

How much discounting is necessary? If one could observe the true utility curve, and therefore calculate xc, the risk premium would be:

        Risk Premium = [ E(x) / xc ] - 1

Mathematically, xc is is the inverse utility function, applied to the investment’s expected utility xc = U-1( E(U) ). On first blush, it would look like the inverse utility function simply “undoes” the utility calculation based on the investment’s performance, but if we remember that E(U) < U( E(x) ), we can see again that xc < E(x).

Getting at the risk premium

Obviously, as nice as it would be to use mathematics to calculate the true risk premium, the problem is that we can’t really observe utility functions in practice, and therefore there is no formula that can truly tell us what risk premium we should really use for our own investments. As investment analysts, however, we might be able to sense our own utility functions, even if it is difficult to map the functions of others.

For example, we can ask ourselves how much we would feel comfortable paying for an investment if we were to receive the investment result by day’s end, rather than at the end of the investment horizon. Doing this focuses our analysis solely on the risk aspect of the investment, rather than confounding the risk with the time aspect. Although an answer by this method is admittedly determined subjectively, it does give us a sense of the appropriate discount to use for the risk premium. We should not be surprised if our “comfortable price” turns out to be less than the investment’s expected value; indeed, we should expect it. How much less gives us the risk premium.

As mentioned, the advantage of this method is that it separates the time component of an investment’s discount factor from its risk component. Normally, when risk factors are estimated, they are “added on top of” the discount factor for time value (a.k.a the risk-free rate). This encourages investment analysts to project the risks further into the future, making risks seem more abstract than they really are. By thinking in terms of an investment result that, while unknown, will be known later today, we can focus our minds specifically on the risk, rather than conflating it with the discount for time. The suggested mechanism is:

1) Evaluate risks as quantitatively as possible, and determine expected value E(x).

2) Determine a risk discount, based on the price, P, you would be comfortable paying for the investment, assuming that the result becomes known and delivered later that same day. Then the risk premium, RP = E(x) / P.

3) Discount P to the present, using the risk-free rate (RFR) as the discount factor for the time value of money.

Working backwards, we see that the discount rate is then constructed as: Discount Rate = RFR + RP .

Future posts on risk premia

This analysis of the origin of risk premia has some additional implications that I want to cover in a future post. Most importantly, it suggests that risk premia may change not simply a result of asset volatility (though it responds to that too), but also can be the result of changing utility curves. The implications of this for investment strategy are many, and I will return to them in a later post.

Why do Risk Premia exist?

When I entered this industry several years ago, I blew my first real interview because I didn’t understand the concept of a risk premium. Ironically, I later heard through the grapevine that I performed well during interview, but I was struggling with my unwillingness to invest as my analysis suggested that I should, and I later wrote an email explaining my discomfort involving stuff from my old probability studies in physics. It apparently was this follow-up letter that struck the interviewer as strange, and he decided to look elsewhere. In retrospect, what was missing from the analysis was a better understanding of risk premiums.

The interviewer asked me how much I should be willing to pay today for a contract where he would pay me $100 in six months if the temperature were above the historical median for that day. The expected value of that bet is fairly simple: $50, and I knew enough from economics to know that the $50 needed to be discounted to the present to come up with the contract’s present value. Assuming that treasuries were yielding 4%, the contract would seem to be worth $49 today.

Although I felt comfortable with the analysis, I struggled with the fact that, were I pressed in real life, I would not have been willing to pay $49 for that contract. I was unemployed at the time, and my savings were especially needed, and so I would not have been willing to put that money at risk. That instinct turned out to be the right one, but at the time I did not understand why.

To make the contract attractive, the price would need to be less than $49. If the contract had simply been to pay me $50 (and I was certain it would be honored, and I didn’t need the money before then, and there were no other attractive investment), then $49 would have been more or less the right price. But the interviewer wasn’t going to pay $50; he was going to pay $100, or possibly $0. In other words, there was risk. Risk made me uneasy, even more so, given my conditions at the time. That uneasiness deserves compensation, and it turns out to be appropriate to compensate.

Why is there a risk premium?

A substantial part of financial analysis is about estimating the right premium to compensate an investor for taking on investment risk. To figure a risk premium correctly, it helps to understand why there should be one in the first place.

It turns out that a risk premium is a natural outcome of the economic principle of diminishing utility. Without the jargon, risk premia come from the fact that, although winning $200 is twice as much as just winning $100, and definitely better, it is less than twice as satisfying.

A utility function tells us how “satisfying” it is to have a particular quantity of money or combination of goods. It converts an observable quantity like “dollars in the bank” to the “degree of satisfaction” those dollars confer. Utilities are notoriously difficult to work with in practice, because they cannot be quantified directly, and one person’s utility function, even if it could be observed, may not be comparable to another person’s function (this causes difficulties in welfare economics because it implies that there is no aggregable social welfare function for public policy makers to maximize).

There are two things we know do about utility functions: 1) having more wealth should be preferable to having less (at extreme wealth levels even this might not be true, but that is a subject for a different post), and 2) as one acquires more, additional wealth provides less additional satisfaction, an effect called “decreasing marginal utility.”

There is a rational reason to expect decreasing marginal utility: if I give you $10,000, you are likely to be happy and use it for the things that matter most on your list of wants and needs. If I hand you a second $10,000, you are likely to be even happier, but the things you use it for will be less essential to you than with the first $10,000 you gained, or else you would have attended to them with the first $10k, rather than wait for the second (which presumably you did not know was coming).

The mathematical implication of an increasing utility function with decreasing marginal utility is that a graph of utility vs. wealth should look roughly like figure 1, always growing with wealth, but flattening out and growing more slowly as wealth increases.

[ Click for Figure 1 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig1.jpg”>

The curvature of the utility curve is important, because it is ultimately the reason for the risk premium.

Let’s assume now that we are about to enter a risky investment. To keep it simple, we will have one of two outcomes, with equal likelihood. Either we will get a high payoff, labeled as H on Figure 2, or we will get a low payoff, labeled L on the same figure. Since both payoffs have an equal likelihood of occurring, the expected payoff, E(x), is simply the average of the two outcome, and sits exactly between the the positive and negative outcomes (shown as (x+∂) and (x-∂) on the figure).

[ Click for Figure 2 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig2.jpg”>

Now look at the utilities for this scenario. Just as we can compute expected wealth as the average of H and L’s wealth, we can also compute expected utility by averaging the utility expected at H and L. This utility is also exactly halfway between H’s and L’s utility, and is shown by point A on Figure 2. But point A (the expected utility with risk) delivers less utility (i.e. satisfaction) than the one would get if we were just guaranteed E(x). The fact that we are either going to have (x+∂) or (x-∂) at the end of the investment means that our investment’s expected utility E(U) is less than the utility of the expected outcome U( E[x] ), simply because there is risk involved.

In other words, the expected utility of a risky bet is less than the utility of the bet’s expected value. Mathematically,

        E(U) < U( E(x) )

[ Click for Figure 3 ]

<img src=“http://www.bruce.chadwick.org/blogAssets/RiskPremiumP1/RiskPremiumFig3.jpg”>

Figure 3 goes a step further, and shows that this risky bet has the same expected utility as another wealth outcome, xc, sometimes called the “certainty equivalent” wealth. The certainty equivalent wealth (point C on Figure 3) represents the level of wealth that - if guaranteed - provides the same degree as satisfaction as the expected utility of the risky option. Importantly, because of the way the utility function curves, the certainty equivalent wealth, xc, is always less than the expected wealth, E(x).

Since an investor is really trying to maximize expected utility, not expected wealth, the value of the risky bet to that investor is actually xc, the certainty equivalent, and not E(x), the expected value, because both the certainty equivalent and the risky investment produce the same expected utility.

As a result, it is xc, the certainty equivalent, not E(x), that should be discounted to the present to account for the time value of money, because PV(xc) is the value that, if invested today without any risk, will produce the same expected satisfaction to the investor.

And how do we get from E(x), which we can hope to compute from expected outcomes, to xc, the non-risky equivalent? We discount E(x) by a risk premium to estimate xc.

How much discounting is necessary? If one could observe the true utility curve, and therefore calculate xc, the risk premium would be:

        Risk Premium = [ E(x) / xc ] - 1

Mathematically, xc is is the inverse utility function, applied to the investment’s expected utility xc = U-1( E(U) ). On first blush, it would look like the inverse utility function simply “undoes” the utility calculation based on the investment’s performance, but if we remember that E(U) < U( E(x) ), we can see again that xc < E(x).

Getting at the risk premium

Obviously, as nice as it would be to use mathematics to calculate the true risk premium, the problem is that we can’t really observe utility functions in practice, and therefore there is no formula that can truly tell us what risk premium we should really use for our own investments. As investment analysts, however, we might be able to sense our own utility functions, even if it is difficult to map the functions of others.

For example, we can ask ourselves how much we would feel comfortable paying for an investment if we were to receive the investment result by day’s end, rather than at the end of the investment horizon. Doing this focuses our analysis solely on the risk aspect of the investment, rather than confounding the risk with the time aspect. Although an answer by this method is admittedly determined subjectively, it does give us a sense of the appropriate discount to use for the risk premium. We should not be surprised if our “comfortable price” turns out to be less than the investment’s expected value; indeed, we should expect it. How much less gives us the risk premium.

As mentioned, the advantage of this method is that it separates the time component of an investment’s discount factor from its risk component. Normally, when risk factors are estimated, they are “added on top of” the discount factor for time value (a.k.a the risk-free rate). This encourages investment analysts to project the risks further into the future, making risks seem more abstract than they really are. By thinking in terms of an investment result that, while unknown, will be known later today, we can focus our minds specifically on the risk, rather than conflating it with the discount for time. The suggested mechanism is:

1) Evaluate risks as quantitatively as possible, and determine expected value E(x).

2) Determine a risk discount, based on the price, P, you would be comfortable paying for the investment, assuming that the result becomes known and delivered later that same day. Then the risk premium, RP = E(x) / P.

3) Discount P to the present, using the risk-free rate (RFR) as the discount factor for the time value of money.

Working backwards, we see that the discount rate is then constructed as: Discount Rate = RFR + RP .

Future posts on risk premia

This analysis of the origin of risk premia has some additional implications that I want to cover in a future post. Most importantly, it suggests that risk premia may change not simply a result of asset volatility (though it responds to that too), but also can be the result of changing utility curves. The implications of this for investment strategy are many, and I will return to them in a later post.

Should Ethics be Taught in Business and Finance?

I was watching a televised interview of Warren Buffet and Bill Gates at Columbia University recently and saw Warren Buffet field a question about “whether ethics can be taught [in a business school curriculum].” I frequently talk to college students about the CFA program and its role in a financial career, and get similar questions about the ethics segment of CFA studies. I agreed with Warren Buffet when he said that “ethics should really be taught in the home,” but I was sad that he dodged the question about the role of ethics in business school preparation and accreditations.

In short, I think, “YES,” ethics studies are valuable and can make a difference for business students and the businesses that they run.

It is common to laugh a bit and complain about the ethical situations that are tested on things like the CFA examinations, and it is true that some of the questions asked are maddeningly subjective and difficult to figure out. In defense of the CFA examiners, however, they do not fail candidates if they get some of these questions wrong, and it is theoretically possible to pass the exam without giving a single correct response to any ethics question. I do think it is reasonable to ask potential charterholders to be able to answer most ethics questions correctly, particularly if they are going to receive a charter that - should the holder be found in violation of ethical and professional standards - can be suspended or even revoked.

The more common objection, however, is that passing an ethics course or examination is not going to turn an unethical person into an ethical one. There is indeed comic irony in the image of a bright, confident, attractive student who receives an “A” in business ethics by copying homework in some clever way and cheating on the exams. On this point, I agree: having passed an ethics course, perhaps even with strong marks, is no guarantee that the person passing it is therefore ethical. A true, forward-looking, evaluation of a person’s ethical character must consider many more indicators of behavior than simply whether they passed an examination or took a particular course.

But the rationale for ethics courses in business schools and on credentialing examinations is not really about the transformation of unethical people into ethical ones - though one can hope this might happen in a few cases. Rather, it is about building awareness of the ethical landscape surrounding business issues, understanding how ethical dilemmas arise, and how to deal with them at different stages of their development. The hope is to be able to identify, manage, and perhaps avoid ethical difficulties at early stages, when they are easier to handle, rather than discover them late, panic, and search for the most expedient solution, which may itself be ethically problematic.

There is a big difference between someone who is unethical - willing to break moral and ethical norms for personal gain - and someone who is simply unaware of the ethical dimensions of the decisions they make. The former is unlikely to be reformed by an ethics curriculum, but the latter is likely to gain something from it, and the business community in general will profit by the improvement in the quality of its membership. I have no hard evidence for this, and it may reflect my conservatively optimistic view of human nature, but I would guess that - particularly at early stages in a career - there are many more ethically unaware or neutral students than truly unethical ones, and the ethically unaware do benefit from ethics training.

The ethically unaware and untrained may still engage in unethical behavior, but in these cases, it is often because they have unwittingly stumbled into situations of conflict of interest, of competing pressures from more senior staff, or simple ignorance of the expectations and needs of their supervisors and clients. In these cases, education which focuses on how the conflict evolved, what ethical standards are at stake, what plausible actions can be taken to resolve the situation and avoid it in the future are genuine contributions to the education of new entrants to the professional community.

Even ethically committed may benefit from ethics training just as much as the ethically unaware. Candidates who have, as Warren Buffet said, “learned ethics in the home” can still benefit by learning alternative methods of handling the types conflicts that may not have been apparent before, simply because the context of a business situation may not have been considered much in one’s “home training.” These professionals can also benefit from ethics training because some business profits that might otherwise have been forgone due to an ethical concern may now be realized because of ethical alternatives that have been learned to obtain them. Even those who take their ethics and living an ethical life very seriously are not born knowing how to navigate the complex situations that life and business situations throw at all of us. Ethics training can help to identify these alternatives and create both business and social value in the process.

Although this point can fill several blog posts or even several books, a more ethical business is in fact a less risky business. To the extent that “ethics risk” is an unnecessary risk (i.e. to the extent that there are ethical alternatives to unethical business practices), ethical behavior creates economic, business, and shareholder value. I do not necessarily believe that all unethical business practices have ethical alternatives, but I do think that there is much value to be extracted by substituting ethical for the unethical in many cases. The challenge is that most “ethics risk” is “tail risk,” and so a long period of outperformance by less ethically constrained companies can sometimes make it seem as though ethical constraints are a business liability, particularly in contexts where there is a strong first-mover advantage and/or information is scarce. It is likely that ethical companies perform adequately or even better than unethical on a risk-adjusted basis, but this is a topic for a separate posting.

Ethics courses and ethics requirements will not rid the business community of the truly unethical, but it can turn the ethically unaware into ethically responsible members of society and reduce the number of unintentional ethical breaches that destroy trust, raise the cost of capital (through increased risk premia), and make society less productive. This is the true goal of ethics education in business and credentialing: to create more “virtuous” business participants and a more efficiently functioning economy, and I support it heartily.

Should Ethics be Taught in Business and Finance?

I was watching a televised interview of Warren Buffet and Bill Gates at Columbia University recently and saw Warren Buffet field a question about “whether ethics can be taught [in a business school curriculum].” I frequently talk to college students about the CFA program and its role in a financial career, and get similar questions about the ethics segment of CFA studies. I agreed with Warren Buffet when he said that “ethics should really be taught in the home,” but I was sad that he dodged the question about the role of ethics in business school preparation and accreditations.

In short, I think, “YES,” ethics studies are valuable and can make a difference for business students and the businesses that they run.

It is common to laugh a bit and complain about the ethical situations that are tested on things like the CFA examinations, and it is true that some of the questions asked are maddeningly subjective and difficult to figure out. In defense of the CFA examiners, however, they do not fail candidates if they get some of these questions wrong, and it is theoretically possible to pass the exam without giving a single correct response to any ethics question. I do think it is reasonable to ask potential charterholders to be able to answer most ethics questions correctly, particularly if they are going to receive a charter that - should the holder be found in violation of ethical and professional standards - can be suspended or even revoked.

The more common objection, however, is that passing an ethics course or examination is not going to turn an unethical person into an ethical one. There is indeed comic irony in the image of a bright, confident, attractive student who receives an “A” in business ethics by copying homework in some clever way and cheating on the exams. On this point, I agree: having passed an ethics course, perhaps even with strong marks, is no guarantee that the person passing it is therefore ethical. A true, forward-looking, evaluation of a person’s ethical character must consider many more indicators of behavior than simply whether they passed an examination or took a particular course.

But the rationale for ethics courses in business schools and on credentialing examinations is not really about the transformation of unethical people into ethical ones - though one can hope this might happen in a few cases. Rather, it is about building awareness of the ethical landscape surrounding business issues, understanding how ethical dilemmas arise, and how to deal with them at different stages of their development. The hope is to be able to identify, manage, and perhaps avoid ethical difficulties at early stages, when they are easier to handle, rather than discover them late, panic, and search for the most expedient solution, which may itself be ethically problematic.

There is a big difference between someone who is unethical - willing to break moral and ethical norms for personal gain - and someone who is simply unaware of the ethical dimensions of the decisions they make. The former is unlikely to be reformed by an ethics curriculum, but the latter is likely to gain something from it, and the business community in general will profit by the improvement in the quality of its membership. I have no hard evidence for this, and it may reflect my conservatively optimistic view of human nature, but I would guess that - particularly at early stages in a career - there are many more ethically unaware or neutral students than truly unethical ones, and the ethically unaware do benefit from ethics training.

The ethically unaware and untrained may still engage in unethical behavior, but in these cases, it is often because they have unwittingly stumbled into situations of conflict of interest, of competing pressures from more senior staff, or simple ignorance of the expectations and needs of their supervisors and clients. In these cases, education which focuses on how the conflict evolved, what ethical standards are at stake, what plausible actions can be taken to resolve the situation and avoid it in the future are genuine contributions to the education of new entrants to the professional community.

Even ethically committed may benefit from ethics training just as much as the ethically unaware. Candidates who have, as Warren Buffet said, “learned ethics in the home” can still benefit by learning alternative methods of handling the types conflicts that may not have been apparent before, simply because the context of a business situation may not have been considered much in one’s “home training.” These professionals can also benefit from ethics training because some business profits that might otherwise have been forgone due to an ethical concern may now be realized because of ethical alternatives that have been learned to obtain them. Even those who take their ethics and living an ethical life very seriously are not born knowing how to navigate the complex situations that life and business situations throw at all of us. Ethics training can help to identify these alternatives and create both business and social value in the process.

Although this point can fill several blog posts or even several books, a more ethical business is in fact a less risky business. To the extent that “ethics risk” is an unnecessary risk (i.e. to the extent that there are ethical alternatives to unethical business practices), ethical behavior creates economic, business, and shareholder value. I do not necessarily believe that all unethical business practices have ethical alternatives, but I do think that there is much value to be extracted by substituting ethical for the unethical in many cases. The challenge is that most “ethics risk” is “tail risk,” and so a long period of outperformance by less ethically constrained companies can sometimes make it seem as though ethical constraints are a business liability, particularly in contexts where there is a strong first-mover advantage and/or information is scarce. It is likely that ethical companies perform adequately or even better than unethical on a risk-adjusted basis, but this is a topic for a separate posting.

Ethics courses and ethics requirements will not rid the business community of the truly unethical, but it can turn the ethically unaware into ethically responsible members of society and reduce the number of unintentional ethical breaches that destroy trust, raise the cost of capital (through increased risk premia), and make society less productive. This is the true goal of ethics education in business and credentialing: to create more “virtuous” business participants and a more efficiently functioning economy, and I support it heartily.

Should Ethics be Taught in Business and Finance?

I was watching a televised interview of Warren Buffet and Bill Gates at Columbia University recently and saw Warren Buffet field a question about “whether ethics can be taught [in a business school curriculum].” I frequently talk to college students about the CFA program and its role in a financial career, and get similar questions about the ethics segment of CFA studies. I agreed with Warren Buffet when he said that “ethics should really be taught in the home,” but I was sad that he dodged the question about the role of ethics in business school preparation and accreditations.

In short, I think, “YES,” ethics studies are valuable and can make a difference for business students and the businesses that they run.

It is common to laugh a bit and complain about the ethical situations that are tested on things like the CFA examinations, and it is true that some of the questions asked are maddeningly subjective and difficult to figure out. In defense of the CFA examiners, however, they do not fail candidates if they get some of these questions wrong, and it is theoretically possible to pass the exam without giving a single correct response to any ethics question. I do think it is reasonable to ask potential charterholders to be able to answer most ethics questions correctly, particularly if they are going to receive a charter that - should the holder be found in violation of ethical and professional standards - can be suspended or even revoked.

The more common objection, however, is that passing an ethics course or examination is not going to turn an unethical person into an ethical one. There is indeed comic irony in the image of a bright, confident, attractive student who receives an “A” in business ethics by copying homework in some clever way and cheating on the exams. On this point, I agree: having passed an ethics course, perhaps even with strong marks, is no guarantee that the person passing it is therefore ethical. A true, forward-looking, evaluation of a person’s ethical character must consider many more indicators of behavior than simply whether they passed an examination or took a particular course.

But the rationale for ethics courses in business schools and on credentialing examinations is not really about the transformation of unethical people into ethical ones - though one can hope this might happen in a few cases. Rather, it is about building awareness of the ethical landscape surrounding business issues, understanding how ethical dilemmas arise, and how to deal with them at different stages of their development. The hope is to be able to identify, manage, and perhaps avoid ethical difficulties at early stages, when they are easier to handle, rather than discover them late, panic, and search for the most expedient solution, which may itself be ethically problematic.

There is a big difference between someone who is unethical - willing to break moral and ethical norms for personal gain - and someone who is simply unaware of the ethical dimensions of the decisions they make. The former is unlikely to be reformed by an ethics curriculum, but the latter is likely to gain something from it, and the business community in general will profit by the improvement in the quality of its membership. I have no hard evidence for this, and it may reflect my conservatively optimistic view of human nature, but I would guess that - particularly at early stages in a career - there are many more ethically unaware or neutral students than truly unethical ones, and the ethically unaware do benefit from ethics training.

The ethically unaware and untrained may still engage in unethical behavior, but in these cases, it is often because they have unwittingly stumbled into situations of conflict of interest, of competing pressures from more senior staff, or simple ignorance of the expectations and needs of their supervisors and clients. In these cases, education which focuses on how the conflict evolved, what ethical standards are at stake, what plausible actions can be taken to resolve the situation and avoid it in the future are genuine contributions to the education of new entrants to the professional community.

Even ethically committed may benefit from ethics training just as much as the ethically unaware. Candidates who have, as Warren Buffet said, “learned ethics in the home” can still benefit by learning alternative methods of handling the types conflicts that may not have been apparent before, simply because the context of a business situation may not have been considered much in one’s “home training.” These professionals can also benefit from ethics training because some business profits that might otherwise have been forgone due to an ethical concern may now be realized because of ethical alternatives that have been learned to obtain them. Even those who take their ethics and living an ethical life very seriously are not born knowing how to navigate the complex situations that life and business situations throw at all of us. Ethics training can help to identify these alternatives and create both business and social value in the process.

Although this point can fill several blog posts or even several books, a more ethical business is in fact a less risky business. To the extent that “ethics risk” is an unnecessary risk (i.e. to the extent that there are ethical alternatives to unethical business practices), ethical behavior creates economic, business, and shareholder value. I do not necessarily believe that all unethical business practices have ethical alternatives, but I do think that there is much value to be extracted by substituting ethical for the unethical in many cases. The challenge is that most “ethics risk” is “tail risk,” and so a long period of outperformance by less ethically constrained companies can sometimes make it seem as though ethical constraints are a business liability, particularly in contexts where there is a strong first-mover advantage and/or information is scarce. It is likely that ethical companies perform adequately or even better than unethical on a risk-adjusted basis, but this is a topic for a separate posting.

Ethics courses and ethics requirements will not rid the business community of the truly unethical, but it can turn the ethically unaware into ethically responsible members of society and reduce the number of unintentional ethical breaches that destroy trust, raise the cost of capital (through increased risk premia), and make society less productive. This is the true goal of ethics education in business and credentialing: to create more “virtuous” business participants and a more efficiently functioning economy, and I support it heartily.

A Political Scientist wins the Nobel Prize in Economics

I promised to write about Elinor Ostrom and the significance of the Nobel Prize in Economics, which she shares this year with U.C. Berkeley economist Oliver Williamson. As a political economist myself - and a political economist whose Ph.D. is in Political Science rather than Economics - Ostrom’s selection provides both personal satisfaction and professional validation.

I referenced Ostrom’s work in writing my own dissertation, which focused on how political regimes and processes affected the valuation of environmental goods and services. Her work on common pool resources was key to identifying a middle-ground between the “privatize everything,” and “regulate everything,” solutions to common-pool and environmental issues.

Environmental policy work is one where the lines between economists and policy analysts are often blurred, and one’s disciplinary background might affect some of the approaches used, but it is still necessary for economists to understand the influence of political institutions and for policy analysts to know economics. Yet somehow, when it came time to compete for job assignments, the economists often seem to have had the upper hand.

I once had a client come in screaming at me saying “I thought you were an economist!,” (to which my immediate, but non-verbalized reaction was, “and I thought you could read!”) as if the problems we were tackling were things that a well-trained policy analyst could not handle. It turned out that he was concerned that I might not understand is that project investments should go to projects with the highest marginal profitability, as if this simple concept were unattainable by someone who had not invented a new econometric technique en route to a Ph.D. in economics.

There is a popular illusion that political science is not as rigorous as economics, driven to a large extent by the fact that economics employs more obviously mathematical techniques, and the mathematics makes economics seem more scientific, because the equations make it resemble the hard sciences. But equations do not make something scientific; rather, it is the validation of knowledge through logic, prediction, and experimentation that makes knowledge scientific. Mathematization of economics does help to generate clearer predictions and improve falsifiability, but it tends to create the illusion of a precision which economists do not presently possess.

With respect to political science, there are two misperceptions that appear to handicap us in the public mind. The first is the general perception that political scientists are not quantitative at all. This is simply false, although there are a number of political scientists who are not quantitatively inclined. Votes, budgets, populations, economic data, levels of violence, numbers of conflicts, taxes collected, etc. are all quantifiable and good political scientists know how to handle that data and will use it when applicable.

The second misperception is that because there are many aspects of political behavior and power dynamics that are not quantifiable, political science is therefore less rigorous than fields like physics or chemistry, or even economics. It may be that college graduates in political science may have gravitated to the field because of a desire to escape the quantitative demands of more strictly quantitative fields, but it does not mean that they can escape thinking logically and rigorously, and it certainly does not mean that graduate level students can slide on those issues.

There are two advantages to political science training. One advantage, by comparison with traditional economics, is that political science is encouraged to consider all aspects of a political dynamic, whether they can be quantified or not. I am overgeneralizing a bit here, but traditional quantitative economics, by contrast, will tend to ignore or cast as “exogenous” those things which do not fit neatly into a quantitative model. At any one instance, this may be inconsequential, but successive models may then start to form a beautiful logical coherent whole that describes a world in which there are no things that cannot be quantified, and that world is most certainly not our own.

The second advantage is that good political science training will teach specifically how to evaluate non-quantitative data. To the untrained, it may seem that qualitative work is nothing more than a collection of anecdotes with some subjective spin attached to them, but the fact is that there is logic to the comparative method and how comparisons of even non-quantifiable factors are structured. Some day, I would like to produce a post describing some of these techniques and how they might be applied to the investment process.

So the awarding of the Nobel Prize to a political scientist is satisfying in that it recognizes that economic knowledge does not necessarily reside only in economics Ph.D.s or in maximally quantitative work. Qualitative factors such as institutional design and structure can be important, and - more importantly - their study can be done with both impact and rigor.

This is all the more important these days because the financial crisis has meant that politics is back in markets - in a big way. For nearly 30 years, the main drumbeat in political economy has been to get the state out of economic policy; now, the crisis has made the economy to some extent dependent on state actions, and this is likely to continue. After so much time demonizing state intervention, it is increasingly important to believe that the state *can* have a positive effect on the economy, because if one does not believe this, then there will be no way to separate good economic policy from bad policy in the post-crisis world. And that would be a dangerous thing.

As an addendum, I should add that I know and respect many of my colleagues who are economists. This post is not intended as an attack on economists themselves, but more on the popular perceptions about economists and their value vis-a-vis other highly trained social scientists.

A Political Scientist wins the Nobel Prize in Economics

I promised to write about Elinor Ostrom and the significance of the Nobel Prize in Economics, which she shares this year with U.C. Berkeley economist Oliver Williamson. As a political economist myself - and a political economist whose Ph.D. is in Political Science rather than Economics - Ostrom’s selection provides both personal satisfaction and professional validation.

I referenced Ostrom’s work in writing my own dissertation, which focused on how political regimes and processes affected the valuation of environmental goods and services. Her work on common pool resources was key to identifying a middle-ground between the “privatize everything,” and “regulate everything,” solutions to common-pool and environmental issues.

Environmental policy work is one where the lines between economists and policy analysts are often blurred, and one’s disciplinary background might affect some of the approaches used, but it is still necessary for economists to understand the influence of political institutions and for policy analysts to know economics. Yet somehow, when it came time to compete for job assignments, the economists often seem to have had the upper hand.

I once had a client come in screaming at me saying “I thought you were an economist!,” (to which my immediate, but non-verbalized reaction was, “and I thought you could read!”) as if the problems we were tackling were things that a well-trained policy analyst could not handle. It turned out that he was concerned that I might not understand is that project investments should go to projects with the highest marginal profitability, as if this simple concept were unattainable by someone who had not invented a new econometric technique en route to a Ph.D. in economics.

There is a popular illusion that political science is not as rigorous as economics, driven to a large extent by the fact that economics employs more obviously mathematical techniques, and the mathematics makes economics seem more scientific, because the equations make it resemble the hard sciences. But equations do not make something scientific; rather, it is the validation of knowledge through logic, prediction, and experimentation that makes knowledge scientific. Mathematization of economics does help to generate clearer predictions and improve falsifiability, but it tends to create the illusion of a precision which economists do not presently possess.

With respect to political science, there are two misperceptions that appear to handicap us in the public mind. The first is the general perception that political scientists are not quantitative at all. This is simply false, although there are a number of political scientists who are not quantitatively inclined. Votes, budgets, populations, economic data, levels of violence, numbers of conflicts, taxes collected, etc. are all quantifiable and good political scientists know how to handle that data and will use it when applicable.

The second misperception is that because there are many aspects of political behavior and power dynamics that are not quantifiable, political science is therefore less rigorous than fields like physics or chemistry, or even economics. It may be that college graduates in political science may have gravitated to the field because of a desire to escape the quantitative demands of more strictly quantitative fields, but it does not mean that they can escape thinking logically and rigorously, and it certainly does not mean that graduate level students can slide on those issues.

There are two advantages to political science training. One advantage, by comparison with traditional economics, is that political science is encouraged to consider all aspects of a political dynamic, whether they can be quantified or not. I am overgeneralizing a bit here, but traditional quantitative economics, by contrast, will tend to ignore or cast as “exogenous” those things which do not fit neatly into a quantitative model. At any one instance, this may be inconsequential, but successive models may then start to form a beautiful logical coherent whole that describes a world in which there are no things that cannot be quantified, and that world is most certainly not our own.

The second advantage is that good political science training will teach specifically how to evaluate non-quantitative data. To the untrained, it may seem that qualitative work is nothing more than a collection of anecdotes with some subjective spin attached to them, but the fact is that there is logic to the comparative method and how comparisons of even non-quantifiable factors are structured. Some day, I would like to produce a post describing some of these techniques and how they might be applied to the investment process.

So the awarding of the Nobel Prize to a political scientist is satisfying in that it recognizes that economic knowledge does not necessarily reside only in economics Ph.D.s or in maximally quantitative work. Qualitative factors such as institutional design and structure can be important, and - more importantly - their study can be done with both impact and rigor.

This is all the more important these days because the financial crisis has meant that politics is back in markets - in a big way. For nearly 30 years, the main drumbeat in political economy has been to get the state out of economic policy; now, the crisis has made the economy to some extent dependent on state actions, and this is likely to continue. After so much time demonizing state intervention, it is increasingly important to believe that the state *can* have a positive effect on the economy, because if one does not believe this, then there will be no way to separate good economic policy from bad policy in the post-crisis world. And that would be a dangerous thing.

As an addendum, I should add that I know and respect many of my colleagues who are economists. This post is not intended as an attack on economists themselves, but more on the popular perceptions about economists and their value vis-a-vis other highly trained social scientists.

A Political Scientist wins the Nobel Prize in Economics

I promised to write about Elinor Ostrom and the significance of the Nobel Prize in Economics, which she shares this year with U.C. Berkeley economist Oliver Williamson. As a political economist myself - and a political economist whose Ph.D. is in Political Science rather than Economics - Ostrom’s selection provides both personal satisfaction and professional validation.

I referenced Ostrom’s work in writing my own dissertation, which focused on how political regimes and processes affected the valuation of environmental goods and services. Her work on common pool resources was key to identifying a middle-ground between the “privatize everything,” and “regulate everything,” solutions to common-pool and environmental issues.

Environmental policy work is one where the lines between economists and policy analysts are often blurred, and one’s disciplinary background might affect some of the approaches used, but it is still necessary for economists to understand the influence of political institutions and for policy analysts to know economics. Yet somehow, when it came time to compete for job assignments, the economists often seem to have had the upper hand.

I once had a client come in screaming at me saying “I thought you were an economist!,” (to which my immediate, but non-verbalized reaction was, “and I thought you could read!”) as if the problems we were tackling were things that a well-trained policy analyst could not handle. It turned out that he was concerned that I might not understand is that project investments should go to projects with the highest marginal profitability, as if this simple concept were unattainable by someone who had not invented a new econometric technique en route to a Ph.D. in economics.

There is a popular illusion that political science is not as rigorous as economics, driven to a large extent by the fact that economics employs more obviously mathematical techniques, and the mathematics makes economics seem more scientific, because the equations make it resemble the hard sciences. But equations do not make something scientific; rather, it is the validation of knowledge through logic, prediction, and experimentation that makes knowledge scientific. Mathematization of economics does help to generate clearer predictions and improve falsifiability, but it tends to create the illusion of a precision which economists do not presently possess.

With respect to political science, there are two misperceptions that appear to handicap us in the public mind. The first is the general perception that political scientists are not quantitative at all. This is simply false, although there are a number of political scientists who are not quantitatively inclined. Votes, budgets, populations, economic data, levels of violence, numbers of conflicts, taxes collected, etc. are all quantifiable and good political scientists know how to handle that data and will use it when applicable.

The second misperception is that because there are many aspects of political behavior and power dynamics that are not quantifiable, political science is therefore less rigorous than fields like physics or chemistry, or even economics. It may be that college graduates in political science may have gravitated to the field because of a desire to escape the quantitative demands of more strictly quantitative fields, but it does not mean that they can escape thinking logically and rigorously, and it certainly does not mean that graduate level students can slide on those issues.

There are two advantages to political science training. One advantage, by comparison with traditional economics, is that political science is encouraged to consider all aspects of a political dynamic, whether they can be quantified or not. I am overgeneralizing a bit here, but traditional quantitative economics, by contrast, will tend to ignore or cast as “exogenous” those things which do not fit neatly into a quantitative model. At any one instance, this may be inconsequential, but successive models may then start to form a beautiful logical coherent whole that describes a world in which there are no things that cannot be quantified, and that world is most certainly not our own.

The second advantage is that good political science training will teach specifically how to evaluate non-quantitative data. To the untrained, it may seem that qualitative work is nothing more than a collection of anecdotes with some subjective spin attached to them, but the fact is that there is logic to the comparative method and how comparisons of even non-quantifiable factors are structured. Some day, I would like to produce a post describing some of these techniques and how they might be applied to the investment process.

So the awarding of the Nobel Prize to a political scientist is satisfying in that it recognizes that economic knowledge does not necessarily reside only in economics Ph.D.s or in maximally quantitative work. Qualitative factors such as institutional design and structure can be important, and - more importantly - their study can be done with both impact and rigor.

This is all the more important these days because the financial crisis has meant that politics is back in markets - in a big way. For nearly 30 years, the main drumbeat in political economy has been to get the state out of economic policy; now, the crisis has made the economy to some extent dependent on state actions, and this is likely to continue. After so much time demonizing state intervention, it is increasingly important to believe that the state *can* have a positive effect on the economy, because if one does not believe this, then there will be no way to separate good economic policy from bad policy in the post-crisis world. And that would be a dangerous thing.

As an addendum, I should add that I know and respect many of my colleagues who are economists. This post is not intended as an attack on economists themselves, but more on the popular perceptions about economists and their value vis-a-vis other highly trained social scientists.