When a lot of us were taking our finance courses in undergrad, we all probably were introduced to a statistical concept called The Sharpe Ratio. It was developed by William Sharpe in 1966, and is generally considered to be a measure of the “efficiency” of a portfolio or any other investment. It does this by measuring the return of the investment security against the unit of risk (here measured by standard deviation).
The WSO dictionary has the definition as well, but the formula is excess return (i.e., the return of the investment over the risk free rate measured by US Treasuries) divided by standard deviation.
All of that is pretty basic. But for all the quant/stat monkeys out there, let’s think about how you could potentially manipulate this for other information.
Standard deviation (the denominator of the Sharpe ratio) is useful as an estimate of overall volatility risk, but what does that really mean?
This may sound incredibly obvious, but people don't think about it: volatility cuts both ways, up and down.
Therefore, one could argue that standard deviation may not be telling us everything we need to know, since it doesn’t differentiate between what happens when the price of the security rises as opposed to when it falls. What if you wanted to dig a little deeper into just how risky this investment is?
What if we only wanted to see what an investment return looks like when the prices are going down, i.e., “bad volatility?”
There’s a ratio for that, and it’s called the Sortino Ratio. The only thing that makes it different from the original Sharpe ratio is that you divide by downside deviation rather than standard deviation (which represents total volatility). For investors, this can give a more accurate picture of risk.
But what if you wanted to assess return per unit of systemic or market risk? There’s a variation on Sharpe for that, too.
Divide excess return by the Beta of a portfolio, and you have the Treynor Ratio, which serves as a measure of how exposed the return on the investment is to the risk of the overall market.
Now, go out and impress your interviewers! You’re welcome.
This is good.
These ratios were in my junior year "Investment Analysis" class. Nothing groundbreaking...
i extend the sharpe ratio way beyond finance. i incorporate it into many aspects of daily life. sharpe ratio basically says you can't look at reward alone, you have to adjust it by how much risk you take to get that reward, however you define risk. then you get your risk-adjusted reward to make things A-to-A.
a nice real-world application of the sharpe ratio is the Hot-Crazy scale (for all the HIMYM aficionados). risk-adjusted reward...
I took a graduate engineering course in "Financial Optimization" (it's part of my school's financial engineering graduate program).
In it, we used some calculus and higher level 'optimization techniques' (just complicated mathy and programmy stuff) to optimize relatively simple ratios. So for example, we would regularly try to construct a portfolio that maximizes the Sharpe ratio, or maximizes the Sortino ratio. Or maybe we tried to maximize return subject to a constraint that the 5% VAR had to be above a certain threshhold.
I thought it was interesting that we were going through so much math and computer programming work, to optimize a relatively simple ratio. Surely if we can put in this much work to optimize the portfolio, we can think of something better to optimize than the Sharpe ratio (I mean if we're talking about equities, all that we should really be looking at is alpha and beta anyway).
But then I realized that the Sharpe ratio is part of the language spoken in the finance world - and if you're constructing a fund, you construct that fund to be MARKETABLE to your investors. If you're investors demand a strong Sharpe ratio, you get them a strong Sharpe ratio (even if what they should be looking for is maybe a strong alpha).
Similarly, a fund might face a regulatory requirement that their VAR be above a certain level, so we make this a constraint in our optimization. We KNOW that VAR is not a very good metric to use (doesn't capture the ultimate downside, etc), but to my knowledge, regulators still use it, so financial engineers will constuct portfolios built around it.
[quote=JDimon](I mean if we're talking about equities, all that we should really be looking at is alpha and beta anyway)./quote] if all you're looking at is equities, then optimizing the information ratio (excess returns over volatility of excess returns) might work better. Just need to choose the right benchmark.
You forgot the Omega Measure.
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