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Learning outcomes, after watching this video, you will be able to,

Â one, define some more performance measures such as Sortino ratio and Tail ratio.

Â [MUSIC]

Â So this is a graphical representation of the Sharpe ratio and the squared ratio.

Â Now, we will move on to figure out solutions to the problems I

Â identified with the Sharpe ratio.

Â The first problem is that arithmetic mean is used, which is not truly accurate.

Â The second, of course, is with the volatility in the denominator.

Â It's really upside, as well as downside qualitivity.

Â So now, we are going to look at a couple of ratios.

Â One called the Sortino ratio and

Â the other other called the symmetric downside Sharpe ratio.

Â Now, both of them have the advantage that they fix both of these are highlighted.

Â In the numerator, we have the geometric mean.

Â In the case of the Sortino ratio, what you subtract from the geometric mean is

Â something called the minimum acceptable ratio.

Â That could be zero,

Â that could be the risk-free rate, whatever the analyst might wish to choose.

Â And the SDR Sharpe ratio, almost as a rule, uses the risk-free rate.

Â The other difference from the Sharpe ratio is that in the denominator,

Â these two ratios use something called the downside deviation.

Â If you look at the formula carefully, you will observe that the downside

Â deviation only measures the deviation below the average return and

Â ignores all the deviation or volatility above the arithmetic mean.

Â Notice that this is the way most of us think about risk.

Â For most of us, risk is loss of money that's below average return.

Â Now, the SDR Sharpe ratio has another small issue with it.

Â It has a root 2 factor.

Â A square root of 2 factor in the denominator.

Â That is for technical reasons.

Â So what we need to notice at this point is these two ratios are better at capturing

Â what we think of as the notion of risk, a little bit than their Sharpe Ratio.

Â Now, the final ratio I'm going to be talking about in this section

Â is something called the Tail Ratio.

Â Now, this is a very simple ratio.

Â It takes a percentile number, p, let's say, 90th percentile, and

Â says, what is the average of all returns which are above the 90th

Â percentile during the period under consideration?

Â So if you stack up all the returns, find out the 90th percentile point,

Â obviously, the 10% of returns above that will have a certain average.

Â Now, take that in the numerator and

Â divide that by the average return in the bottom 10%.

Â Since you have chosen 90% on the upside, choose 10% on the downside.

Â So essentially, what this is telling you is I am going to give you a ratio of

Â the best month, the best 10% month, to the worst 10% months.

Â And you want to see where the variation of this fund's returns are coming from.

Â Obviously, the higher this ratio, the better the fund's performance.

Â Now, stand alone, this is not great.

Â But it's very useful as an agent to other measures.

Â And I'm going to run you through a quick example.

Â I'm going to just show you a graph across 73 months of two funds,

Â hypothetical funds A and B.

Â Notice the important thing, that both of them start off at the hypothetical value

Â of 1000 and both of them end up, 73 months later, at this hypothetical value of 2000.

Â Which is to say, for somebody who has and investment horizon of 73 months or more,

Â both of these funds might look identical,

Â in the sense that they start from the same point and take you to the same point.

Â But it is not where you have traveled from and where you have traveling to.

Â It is also how bumpy the ride has been throughout, right?

Â In other words, we care about risk.

Â Now, just have a look at this graph and tell me what you think, in your own mind

Â or at least make up your mind, as to what you think is the riskier fund, A or B?

Â And most of us would agree that A has a lot of big hills, ups and downs, right?

Â And B seems to sort of coursed along, and then go up, and then some,

Â and go up again, right?

Â Now, in fact, if you work out the standard deviation of these two funds,

Â it turns out that B has the highest standard deviation.

Â Now, notice that the arithmetic,

Â as well as geometric means of these two funds are going to be almost the same.

Â The geometric mean, for sure, is going to identical because you started at the same

Â point and ended at the same same point.

Â It turns out that arithmetic mean is roughly the same also.

Â But given that B has the highest standard deviation, if you use Sharpe ratio,

Â you would conclude that A is the better performing fund than B.

Â 5:06

But then, if you look at downside deviation and proceed to calculate

Â the Sortino ratio or the SDR Sharpe ratio, or the symmetric downside Sharpe ratio,

Â what you will find is that the conclusion is reversed.

Â Because now, you confirm in numbers what you saw for

Â yourself in the picture, which is that most of the volatility of fund B

Â is really on the upside rather than downside.

Â And for fund A, volatility is upside, as well as downside.

Â So that's a real big take away here.

Â And by the way, if you calculate the tail ratio here,

Â you will also find that fund B does better than fund A on that round also.

Â So what we conclude from this small example is that traditional measures

Â such as to alpha are hopeless as detecting timing ability.

Â So here, we have a manager who's showing timing ability.

Â Clearly, he's reaching the beta of his fund

Â in response to anticipated market conditions.

Â However, traditional alpha or beta measures are not capturing his ability.

Â