0:10

Learning outcomes.

Â After watching this video,

Â you will be able to,

Â one, understand why there is a need to measure performance.

Â Two, define Sharpe ratio.

Â Three, list down the issues with Sharpe measure.

Â The next part of this lecture is all about performance measurement.

Â Now performance measurement, as opposed to the previous section,

Â is relevant to everybody,

Â not just to students of finance.

Â And I will connect efficient markets to performance measurement very quickly.

Â But before we do that,

Â let's understand what is performance measurement.

Â Essentially what we are saying is,

Â there is a bunch of us who invest in

Â notably equity markets or stock markets through vehicles called mutual funds.

Â Now these mutual funds come in two flavors: active and passive.

Â Active mutual funds are those mutual funds which believe that they can,

Â again, process or acquire information smarter.

Â They're smarter than everybody else,

Â so they can earn more money than what the average market return is.

Â Now, passive mutual funds are those that seek to mimic a certain index.

Â So, for example, there are S&P index funds which have

Â the sole purpose of mimicking the return on the S&P 500.

Â Essentially, if the S&P 500 goes up five percent,

Â this fund aims to go up five percent too.

Â Now, where do the active and passive mutual funds come from?

Â Where do these philosophies come from?

Â They come directly from what we talked about just now,

Â which is the market deficiency idea.

Â If you believe, let us say,

Â that markets are largely efficient or,

Â close to 100 percent efficient,

Â then the idea is obviously getting information, processing it,

Â hiring fund managers and so on,

Â is not going to buy you much by way of extra return.

Â In which case you would say,

Â I would go for a passive mutual fund,

Â which is to say, I will be a passive indexer.

Â I will just put my money into an S&P 500 fund,

Â and let the money ride according to the fortunes of the S&P 500.

Â However, if I believe that

Â a particular manager is really exceptional at beating the market,

Â I would actually go and invest my money with an active mutual fund manager.

Â These ideas are closely connected to the efficiency of the market.

Â Now, in terms of active management,

Â there's about $10 trillion under active management in the U.S. alone.

Â In India for example,

Â that number is about $200 billion.

Â Now, obviously these active fund manager,

Â if you believe that he can outperform the market,

Â and deliver you an extra market return,

Â he or she is obviously going to charge you a fee.

Â Now, these fees are typically obviously higher for

Â active mutual fund managers compared to passive mutual fund managers.

Â Now, let's assume an average fee of 0.4 percent.

Â If you think about the $10 trillion number I just stated,

Â you would see that investors spend upwards of about $40 billion.

Â And this is $40 billion,

Â with a B, on fees to these fund managers.

Â Now, if you are in aggregate paying these guys a lot of money,

Â now we need to actually go back and investigate and figure out,

Â are these guys making money for me?

Â Because unless they're making money for me,

Â I will not be willing to part with the fee for the management of the fund.

Â Now, there's a battery of measures which is used to test

Â whether a particular fund/fund manager has done better or worse than the market.

Â These come from the theory that we have studied called Mean-Variance theory.

Â The first measure I'm going to talk about is something called the Sharpe measure.

Â The Sharpe measure is very simply an average return on the fund,

Â so R_P bar is simply the return on a particular fund.

Â R_F bar is the average risk-free rate over the same period.

Â So take the average return of the fund,

Â subtract the average risk-free rate.

Â That's how much you earn over the risk-free rate.

Â Now divide that by the standard deviation of the portfolio's return, or the funds return.

Â And what do you get you get?

Â You get something which is very clearly a reward-to-risk ratio.

Â This particular reward-to-risk ratio is called the Sharpe ratio;

Â a Sharpe measure to be more precise.

Â Now, suppose we do this with a bunch of funds.

Â Obviously, if there is a fund which has

Â a Sharpe ratio of five and another fund which has a sharp ratio of two,

Â obviously the one with the Sharpe ratio of five is set to perform better because,

Â for the same risk it's giving you a higher reward.

Â So essentially it's a standardized reward-to-risk ratio.

Â Now, in isolation this number five,

Â or three, or two, what does it mean?

Â Well, there are statistics that can test

Â whether you are performing better than a particular benchmark.

Â So I could just as well take the Sharpe ratio off a particular index.

Â Let's say there are simply 500 index.

Â In other words, take the average returns on the S&P,

Â subtract the average risk-free rate,

Â divided by the standard deviation of the S&P.

Â And then, compare that to the Sharpe ratio of a fund.

Â Then I'm in a position to figure it out,

Â using the Sharpe measure,

Â whether my particular fund,

Â or my particular portfolio,

Â has actually beaten the index or not.

Â Now, the Sharpe measure,

Â as you might notice, has two immediate problems.

Â Number one, the numerator contains the average fund performance;

Â what I call R_P bar. What is that?

Â It's simply an arithmetic average of about 60 months,

Â or 48 months, or 12 months of the fund returns.

Â So arithmetic averages can be notoriously misleading.

Â Think of a situation where you have $100 to begin with.

Â You have a 50 percent gain in year one that takes you to 150,

Â and a 50 percent loss in year two.

Â That means your 150 has gone down to 75 at the end of year two.

Â Which means over the two years what has happened is,

Â your 100 has become 75,

Â which is a net loss of 25 percent.

Â But if you take the arithmetic average of the two returns over the two years,

Â 50 percent, negative 50 percent,

Â average the two, you get zero.

Â So basically arithmetic average is not

Â a true or accurate measure of the overall return over this period.

Â Now, after all, investors really care about overall returns.

Â They don't really care about the arithmetic average.

Â That's something a statistician would be interested in, not an investor.

Â So that's an issue with the numerator.

Â With the denominator, we have a slightly tangled issue,

Â which is that in the denominator we have

Â the standard deviation. What is standard deviation?

Â It's simply a measure of how spread out

Â the distribution of returns is around the mean or average value.

Â Now, obviously, you can see this most clearly in a normal distribution where,

Â if you have a tight normal distribution around the expected value or average,

Â versus a more spread out distribution,

Â typically we say the more spread out

Â distribution has a higher variance or standard deviation.

Â Notice that the variance or standard deviation,

Â which we're calling volatility here,

Â is really a measure of uncertainty.

Â What we really want in the denominator is a measure of risk.

Â Now, by using standard deviation in the denominator,

Â what we're doing is,

Â we are essentially saying volatility equals uncertainty equals risk.

Â Now, uncertainty statistically is indeed standard deviation,

Â but it is not risk in the way usually investors understand it.

Â What is risk to you?

Â If you think for a moment,

Â what you will find is,

Â risk is really the loss of losing principle.

Â In fact, if I perform better than average,

Â it would still be counted in the standard deviation calculation,

Â but that upside volatility is really not

Â something that I traditionally think of as risk in my portfolio.

Â What I really think of risk,

Â or what I fear most in a portfolio context, is the downside.

Â That is the possibility that I might perform below average.

Â So we need to fix that too.

Â And several measures have been suggested to fix this,

Â and we will discuss this soon.

Â