>> 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