0:31

So, Jensen, Michael Jensen,

created this measure of performance in 1968.

He wanted a way to asses mutual funds,

0:45

mutual fund managers, to see how well they were outperforming the market.

Now a reason for this, one reason they needed a measure,

is sometimes mutual fund managers would invest in high beta stocks,

in other words, volatile stocks with regard to the market.

And they would show high returns, which is good, of course.

But the question is, were

those returns just merely because they were investing in high beta stocks?

And how could we measure the advantage that the fund

manager was providing besides just investing in high beta stocks?

And this measure is referred to as Alpha.

Now in order to understand Alpha,

we need to look back at the capital assets pricing model.

1:50

In particular, I had not been listing the risk free rate and

some people had mentioned this in the forums.

So let's put risk free rate in.

Now right now, the risk free rate is very close to zero, and

so that's one reason that it was left out before.

But, anyways, let's look at this statement of the capital assets pricing model.

It says, going from left to right here, using that equation, and

this is grabbed from Wikipedia, by the way.

So thanks, Wikipedia.

So the expected return on our investment is equal to the risk free rate

plus the beta of our investment with regard to the market,

times the expected return on the market, minus the risk free rate.

So I've got a little bit of notation there below.

The E parentheses means expected R sub i is return on investment,

so E parentheses R sub i is our expected return on the investment.

R sub m is the market return, R sub f is the risk free rate.

Now as I said, for all practical purposes these days you can

drop the risk free rate, because it's so close to zero.

But interest rates may come up soon, and it may make sense to add this back in.

So, anyway just kind of simplifying it the way we've used it so

far, we've been saying the expected return on the investment is equal to beta

times the expected return on the market.

Okay, so that's just recapping CAPM.

Now, let's let's think about that graphically.

3:34

One thing this statement of CAPM says, and remember I mentioned it a moment ago,

maybe people were just investing in high beta stocks.

Let's assume a positive market, we anticipate positive return in the market.

3:49

This line represents our expected return according to beta.

So if beta is larger, and

we have a positive market, the larger the beta, the larger our expected return.

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Now this line crosses through the y-axis

here above zero and the reason for that is,

well, let's suppose we had a zero beta portfolio.

Well, presumably, we're earning interest on our money

even if we're not getting returns based on the market.

And so that interest rate is the risk free rate of return, and so

that's why it's above zero.

Now, these days that risk free rate of return is about zero.

So this line actually normally would go,

we would expect to go through the origin because risk for rate is zero and

the only way we can get return these days is by investing in the market.

4:59

Okay, so that's a statement of capital assets pricing model and

looking at it in terms of our expected return versus beta.

Also note that as our beta becomes

smaller, the smaller the expected return.

If beta is negative in an upward market, of course, we're gonna make less,

and perhaps negative, return, if it's an upward market.

5:31

Okay, now let's move from that theoretical,

expected view to let's look back at actual returns,

and look at an equation that will express that.

Okay, so our actual return on the investment,

if we believe the capital assets pricing model, is equal to the risk free return,

plus beta, times return on the market, minus risk free return.

Now, if we took actual data for an actual equity and

compared it to the market, say the S&P 500, we will usually

find that this doesn't exactly add up.

That's where alpha comes in and we'll get to that in just a second.

6:26

There's an ETF called SPLV.

It's a low volatility member of the S&P 500.

And this is the performance in blue of

SPLV this year to date, 2013,

versus S&P 500 here in red.

Now as you can see, SPLV is,

in terms of cumulative return, is outperforming the market.

6:57

Interestingly though, its beta is 0.75.

So we're in a positive market, upward market.

We've got a beta less than 1,

which would make us believe that our return should not be as high as

the market, yet our cumulative returns are higher than the market.

CAPM predicts that they should be lower,

as you can see by the chart there.

Okay, how might we explain that?

7:40

And that's where we collect these excess returns that are larger

than the returns you would expect with a beta of 0.75.

Now capital assets pricing model says that our expected value of alpha is 0.

And if it's above 0, or below 0, that's due to noise or random chance.

Now, others, like Jensen, assert that, well, this alpha is

actually a representation of the skill of the portfolio manager.

8:42

we've plotted a single dot for the daily return on

SPLV, versus SPY, which is S&P 500.

So for instance, on this day the S&P 500 was up 0.4%,

and SPLV was up about 0.89%.

So it was a great day for SPLV, good day for the market, also.

9:16

it, it turns out that that line, the slope of that line, is beta.

In this case it's about 0.75.

And the place where it intercepts

the y-axis there is alpha.

That's the additional on average return

that SPLV so far this year has provided above the market.

And so that's alpha for SPLV compared to S&P 500.

Now, in order to generate this plot with full correctness, you have to

10:10

Bigger alpha means potentially a bigger portfolio manager skill.

Alpha of zero means that you're getting the returns you would expect for

the risk in your portfolio, namely for a particular beta.

If your alpha is zero that means,

yeah, you may be getting returns greater then the market, but

you're getting about what we would expect for the risk that you're taking.

And again if alpha is positive that indicates,

at least potentially, portfolio manager skill.

If alpha is negative,

that means you might be losing money, the manager might not be skillful.

Okay, thanks very much, and see you again soon.

Bye-bye.