I'd like to talk about the performance evaluation. One of the main applications of financial theory is the actual reward of managers or replacing of manages for performance or underperformance. We've already developed the tools whereby we can go through and do a reasonable first cut at the performance evaluation problem. For example, one thing that we've looked at is something that's referred to as the sharp measure. I didn't call it this before, but let me to find the sharp measure as expected excess return on a security or portfolio divided by its volatility. 

Now the sharp measure gives us a reward to risk ratio. However, let's be careful about what we refer to as risk. In the denominator of the sharp measure is the volatility of that particular asset or project. So in order for this to be risk, it must be the case of looking at projects that are mutually exclusive, that means you can either do one or the other, and we assume that you do not hold that diversified portfolio. So the sharp measure is only a valid measure of performance evaluation when we're talking about mutually exclusive situations. It's expected excess return divided by the volatility. The simple measured calculate and hear practitioners' talking about sharp measures all the time. Of course the major shortcoming with the sharp measure is that it looks at the volatility of the particular asset and refers to that as the risk. We could improve upon this particular measure by looking at a different type of performance evaluation measure and that's what I manna do next. 

What we can do is to look at the performance evaluation in the context of an arithmetic model. So the arithmetic model delivers the data for the security or the portfolio and there's a risk preem that's associated with the data. We multiply the two together and we get the expected return on a project given the level of risk. Now there's a realized return. We compare the realized return to the actual return and we get a difference, which is been called the performance. If the realized return exceeds what is expected given the level of risk, then we say that this asset or this manager has performed better than expected given the level of risk. Sometimes we call this the alpha. And we always look for positive alpha and sometimes people lose and talking about alpha and will say, you know, I'm no alpha manager. Well, I think it's better to be known as a positive alpha manager. You want to achieve a return over and above what is expected given the level of risk. So we're always looking for alpha. And the alpha concept was first introduced by Michael Jensen in his dissertation, 1969. And Jensen studied the performance of a number of mutual funds, and he measured their alphas in the lecture note, there's original graph from Jenson's studies. And he noticed that the performance of these mutual fund managers was less than distinguished, that most of the outputs were negative. A few were positive but there's only one that was significantly positive in its statistical sense. 

There're some other hybrid measures of performance. There's a measure that, um, kind of looks like the sharp measure, and it's called the Trainer measure, named after Dr. Jack Trainer. And it is the expected excess return on the security divided by its beta. It actually makes a lot of sense, because remember we said that one of the problems with the sharp measure was that the denominator had a measure of risk that maybe wasn't measured but was really wanted to consider, especially with a diversified portfolio. Well, this other measure, divides by the beta, and that is the risk. That is the contribution of the security or the portfolio to the variance of large portfolio. So this measure makes a lot of sense. 

There's a lot of other measures I'd details in my lecture notes, but I'll talk about one measure that has got some recent play and actually I'm part of this measure, so it's a little embarrassing talking about it. But it's, was known, I guess now it's the Gram Harby measure. So let me talk about that.

We can think about the sharp measure. Let's go back to the sharp measure in the following context. Think of the efficient frontier and think of the tangency portfolio. Let's call out the Standard Course 500 portfolio. And then we can connect the line from the risk-free rate to that market portfolio and that is the market sharp ratio. It's the best possible sharp ratio that you can obtain given us a tangency portfolio. It's best in the sense that it's got the highest possible slope. And the highest possible slope means that you get the maximum expected return per unit of risk and risk in this context is the variance of the well diversified portfolio. All of the efficient frontier portfolios are well diversified and we're getting the maximum reward per unit of risk and this is exactly the ratio that goes into the capitalized price model. This is the way that data is rewarded in that we're assuming that people hold well diversified portfolios. So the sharp ratio for the market is very important. Now, that's said, if we look at sharp ratios for individual securities, Hardy mentioned that this could be a little problematic, because we're looking at the variance as the risk. And it's possible that a number of these portfolios have sharp ratios that are less than the market sharp ratio. 

So Gram and I come along with the following idea: what we do is, we say, ok, here's a security or portfolio, and actually our application is a bunch of managers that are making recommendations for portfolios. And that's my newsletters. So we looked at the recommendations and looked at the portfolio that are obtained from that. That portfolio's got expected return, and that portfolio's got a variance, or standard deviation. So this is what we do. We form a portfolio of the market, Standard Course 500 or the Morgan Stanley world portfolio. Whatever you want to find is the market. So we form a portfolio that has got exactly the same volatility as the strategy that the managers recommended. And that portfolio's got expected return, our manager's got some return that's realized and we take the difference between the two returns. And we call that the Gram Harby Measure One. 

Let me rewind just a little bit. We're looking at a strategy that is produced standard deviation and expected return. Let's say the standard deviation is 20% and the expected return or the realized return was 15% over this manager's tenure.


Homework


I would like to talk about the performance evaluation. One of the main applications of financial theory is the actual reward of managers or replacing of manages for performance or underperformance. 

We have already developed the tools whereby we can go through and do a reasonable first cut at the performance evaluation problem. For example, one thing that we've looked at is something that's referred to as the sharp measure. I didn't call it this before, but let me to find the sharp measure as expected excess return on a security or portfolio divided by its volatility. Now the sharp measure gives us a reward to risk ratio. However, let's be careful about what we refer to as risk. In the denominator of the sharp measure is the volatility of that particular asset or project. So in order for this to be risk, it must be the case of looking at projects that are mutually exclusive, that means you can either do one or the other, and we assume that you do not hold that diversified portfolio. So the sharp measure is only a valid measure of performance evaluation when we're talking about mutually exclusive situations. It's expected excess return divided by the volatility. 

The simple measured calculate and hear practitioners' talking about sharp measures all the time. Of course the major shortcoming with the sharp measure is that it looks at the volatility of the particular asset and refers to that as the risk. We could improve upon this particular measure by looking at a different type of performance evaluation measure and that's what I manna do next. what we can do is to look at the performance evaluation in the context of an arithmetic model. So the arithmetic model delivers the data for the security or the portfolio and there's a risk preem that's associated with the data. We multiply the two together and we get the expected return on a project given the level of risk.

Now there's a realized return. We compare the realized return to the actual return and we get a difference, which is been called the performance. If the realized return exceeds what is expected given the level of risk, then we say that this asset or this manager has performed better than expected given the level of risk. Sometimes we call this the alpha. And we always look for positive alpha and sometimes people lose and talking about alpha and will say, you know, I'm no alpha manager. Well, I think it's better to be known as a positive alpha manager. You want to achieve a return over and above what is expected given the level of risk. So we're always looking for alpha. And the alpha concept was first introduced by Michael Jensen in his dissertation, 1969. And Jensen studied the performance of a number of mutual funds, and he measured their alphas in the lecture note, there's original graph from Jenson's studies. And he noticed that the performance of these mutual fund managers was less than distinguished, that most of the outputs were negative. A few were positive but there's only one that was significantly positive in its statistical sense. 

There're some other hybrid measures of performance. There's a measure that, um, kind of looks like the sharp measure, and it's called the Trainer measure, named after Dr. Jack Trainer. And it is the expected excess return on the security divided by its beta. It actually makes a lot of sense, because remember we said that one of the problems with the sharp measure was that the denominator had a measure of risk that maybe wasn't measured but was really wanted to consider, especially with a diversified portfolio. Well, this other measure, divides by the beta, and that is the risk. That is the contribution of the security or the portfolio to the variance of large portfolio. So this measure makes a lot of sense. 

There's a lot of other measures I'd details in my lecture notes, but I'll talk about one measure that has got some recent play and actually I'm part of this measure, so it's a little embarrassing talking about it. But it's, was known, I guess now it's the Gram Harby measure. So let me talk about that.

We can think about the sharp measure. Let's go back to the sharp measure in the following context. Think of the efficient frontier and think of the tangency portfolio. Let's call out the Standard Course 500 portfolio. And then we can connect the line from the risk-free rate to that market portfolio and that is the market sharp ratio. It's the best possible sharp ratio that you can obtain given us a tangency portfolio. It's best in the sense that it's got the highest possible slope. And the highest possible slope means that you get the maximum expected return per unit of risk and risk in this context is the variance of the well diversified portfolio. 

All of the efficient frontier portfolios are well diversified and we're getting the maximum reward per unit of risk and this is exactly the ratio that goes into the capitalized price model. This is the way that data is rewarded in that we're assuming that people hold well diversified portfolios. So the sharp ratio for the market is very important. Now, that's said, if we look at sharp ratios for individual securities, Hardy mentioned that this could be a little problematic, because we're looking at the variance as the risk. And it's possible that a number of these portfolios have sharp ratios that are less than the market sharp ratio. So Gram and I come along with the following idea: what we do is, we say, ok, here's a security or portfolio, and actually our application is a bunch of managers that are making recommendations for portfolios. And that's my newsletters. 

So we looked at the recommendations and looked at the portfolio that are obtained from that. That portfolio's got expected return, and that portfolio's got a variance, or standard deviation. So this is what we do. We form a portfolio of the market, Standard Course 500 or the Morgan Stanley world portfolio. Whatever you want to find is the market. So we form a portfolio that has got exactly the same volatility as the strategy that the managers recommended. And that portfolio's got expected return, our manager's got some return that's realized and we take the difference between the two returns. And we call that the Gram Harby Measure One. 

Let me rewind just a little bit. We're looking at a strategy that is produced standard deviation and expected return. Let's say the standard deviation is 20% and the expected return or the realized return was 15% over this manager's tenure.