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

which is a variant of Sharpe ratio.

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

squared answer, after plugging it into the formula etcetera.

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

it has a one to one correspondence.

And my M squared measure is positive, my meaning,

my fund's M squared measure is positive.

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

whatever the benchmark might be.

So there are other measures, but

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

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

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

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

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

There other measures and people will argue, but

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

But it's really systematic risk,

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

Now the moment I put beta in the denominator,

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

it's reward to systematic risk.

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

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

With respect to some benchmark, right?

And the choice of benchmark is still an issue, so

if you leave a fund manager to calculate his so

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

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

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

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

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

that's really the problem here.

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

under-performance measure is Jensen's alpha.

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

and it's a very simple idea.

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

linear regression of my portfolio or

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

Now the intercept in that regression is essentially the alpha.

The idea is, after controlling for

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

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

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

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

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

that's frequently called a positive alpha, right?

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

It means that this managerial period of observation has

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

Now this is a very popular measure and

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

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

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

on the right hand side.

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

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

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

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Now there is yet

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

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

divide that by omega.

And what is omega?

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

It turns out this appraisal ratio is very useful

in ranking funds in the following context.

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

that is in an index fund.

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

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

It turns out the benefit I can get

from potentially moving a little bit into an active fund.

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

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

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

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Well, it depends on your particular purpose.

If your portfolio is your entire retirement fund,

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

And clearly the total risk is the most relevant measure.

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

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

If you're looking for

a small amount of investment in an actively managed fund while

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

Then you would use something called an appraisal ratio.

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

Which means when the portfolio represents

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

So each one has its utility depending on the context.

Now in terms of portfolio manager compensation,

which is what we started this lecture with.

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

Now Jensen's alpha is used widely.

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

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

The question you have to ask yourself is,

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

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

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

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

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

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

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

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

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

past performance is going to continue in the future.

Now as I hinted at this before,

is past performance an indicator of future performance?

Most likely, no, we never know.

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

There have been a few through history, but

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

In any case,

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

This is what I meant when I said,

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

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

I hope you do, and you invest.

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

how much your manager is working for you.

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

how much are you going to end up with.

So this is the basic idea in portfolio manager compensation.