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>> But before we go there, there is a simple measure,

Â which is a variant of Sharpe ratio.

Â The only difference between Sharpe ratio and M squared is that the M

Â squared answer, after plugging it into the formula etcetera.

Â Is going to basically end up giving me a percentage number, so

Â it has a one to one correspondence.

Â And my M squared measure is positive, my meaning,

Â my fund's M squared measure is positive.

Â It means that my Sharpe ratio is higher than that of the benchmark,

Â whatever the benchmark might be.

Â So there are other measures, but

Â the first two measures can be encapsulated in this graph very simply.

Â You will see that you will be reminded of your old mean radiance frontiers and

Â mean standard deviation diagrams when you look at this sort of measure.

Â So essentially, a Sharpe Measure higher than that of the benchmark

Â corresponds to a positive M squared measure, and vice versa.

Â There other measures and people will argue, but

Â what really belongs in the denominator is not sigma or volatility.

Â But it's really systematic risk,

Â which as we all know is represented in finance by the quantity beta.

Â Now the moment I put beta in the denominator,

Â that's really saying that my reward to risk ratio is not reward to total risk,

Â it's reward to systematic risk.

Â Now once I come to this ratio, remember that in the bottom, I have a beta.

Â The moment I have a beta, you have to ask the question, beta with respect to what?

Â With respect to some benchmark, right?

Â And the choice of benchmark is still an issue, so

Â if you leave a fund manager to calculate his so

Â called Treynor measure which is exactly this reward to systematic risk ratio.

Â Now it's really they will choose the benchmark which gives them the lowest beta

Â in the denominator, which in turn will give them the highest Treynor measure.

Â So in other words, this is open to a little bit of manipulation, if you will.

Â If it's too strong a word for you, think about subjectivity off benchmark,

Â that's really the problem here.

Â Perhaps the most popular and often encountered fund out-performance or

Â under-performance measure is Jensen's alpha.

Â After Michael Jensen, who first came up with the measure,

Â and it's a very simple idea.

Â The basic idea is to run a regression, a standard,

Â linear regression of my portfolio or

Â fund return on the left hand side, and the benchmark on the right hand side.

Â Now the intercept in that regression is essentially the alpha.

Â The idea is, after controlling for

Â the beta, that is the systematic risk on the right hand side,

Â is there any systematic out-performance, or under performance?

Â In other words, if alpha is say 0.5% per year, we can

Â 3:26

confidently say after recounting for the beta of this particular fund.

Â This fund out-performs a market by 0.5% per year and

Â that's frequently called a positive alpha, right?

Â And of course the reverse is true too, if alpha is negative 0.5%.

Â It means that this managerial period of observation has

Â under-performed the index or the benchmark by 0.5% per year.

Â Now this is a very popular measure and

Â we can run this very easily in a simple linear regression.

Â Even Excel will do it, you don't need a fancy statistical package.

Â The only issue as I pointed out before is what is the benchmark

Â on the right hand side.

Â This is something we need to think about, but alpha is very popular on Wall Street.

Â And in fact if you ask a fund manager what he's looking for,

Â he's going to perhaps 9 out of 10 reply, I'm looking for positive alpha.

Â 4:26

Now there is yet

Â another measure called appraisal ratio, defined simply as the alpha.

Â That's simply the alpha just talked about, the Jensen's alpha, and

Â divide that by omega.

Â And what is omega?

Â Omega is simply a measure of idiosyncratic risk of the particular fund, all right?

Â It turns out this appraisal ratio is very useful

Â in ranking funds in the following context.

Â So suppose a large portion of my portfolio is a benchmark fund,

Â that is in an index fund.

Â And I am looking not to move entirely into active managed funds, but I am looking to

Â pick amongst actively managed funds to add as a small part of my portfolio.

Â It turns out the benefit I can get

Â from potentially moving a little bit into an active fund.

Â Whereas a large part of my portfolio is in an index fund

Â is given by the appraisal ratio, so essentially it's a ranking tool.

Â So, the point I'm trying to make is when is each method used?

Â 5:30

Well, it depends on your particular purpose.

Â If your portfolio is your entire retirement fund,

Â then obviously that's your entire money, your life savings.

Â And clearly the total risk is the most relevant measure.

Â With all it's problems, Sharpe measure would be the best thing to use there.

Â And we'll come up with variants of Sharpe ratio very soon.

Â If you're looking for

Â a small amount of investment in an actively managed fund while

Â having a large part of your portfolio in an index fund, as I said before.

Â Then you would use something called an appraisal ratio.

Â Now the Treynor measure is obviously used when systematic risk is relevant.

Â Which means when the portfolio represents

Â one of the many active portfolios that are being mixed with a passive benchmark.

Â So each one has its utility depending on the context.

Â Now in terms of portfolio manager compensation,

Â which is what we started this lecture with.

Â In other words we try to look at, how much are you paying these fund managers?

Â Now Jensen's alpha is used widely.

Â So suppose I say, the Jensen's alpha of a particular fund,

Â with respect to an appropriate benchmark, let us say, is 1% per year.

Â The question you have to ask yourself is,

Â what is the compensation that I am willing to pay to this portfolio manager?

Â Well, he would like to keep as much of the 1% with himself, as fees.

Â Naturally, you would like as much of the 1% as possible with you.

Â Naturally, he has to be compensated for his efforts, so

Â we're going to part with some fraction of the 1%.

Â So in other words, the Jensen's alpha represents an upper bound

Â on the amount I'm willing to pay the fund manager as compensation.

Â But the danger with alpha, or any of these measures for

Â that matter, is that the implicit assumption here is that somehow

Â past performance is going to continue in the future.

Â Now as I hinted at this before,

Â is past performance an indicator of future performance?

Â Most likely, no, we never know.

Â Unless you have a super consistent fund manager, there are a few.

Â There have been a few through history, but

Â in most cases past performance is not necessarily an indicator of the future.

Â In any case,

Â it is wise to remember this as a warning in our personal investment portfolios.

Â This is what I meant when I said,

Â this is the part of the lecture which is relevant to all of us.

Â Whether you're a finance graduate or not, as long as you make money, and

Â I hope you do, and you invest.

Â These measures are relevant to the extent that you want to understand

Â how much your manager is working for you.

Â Which in turn means how your money is going to grow, and

Â how much are you going to end up with.

Â So this is the basic idea in portfolio manager compensation.

Â