sortino and beta

I’m getting good results by ranking ETFs by Sortino. I’ve also divided the Sortino by the beta and ranked it that way with good results. Is my logic correct in thinking that with this ratio you are buying the asset with a good risk profile (sortino) and low volatility (beta)? The higher the ration the better the risk/volatility profile is.

Any thoughts out there?

Can you show us the sim?

The Sortino ratio is basically the mean return divided by the downside volatility. It’s very similar to the Sharpe ratio, except that the Sharpe ratio uses total volatility rather than downside volatility. Both of them have the same fundamental problems too:

a) When the standard deviation is significantly less than the mean, the formula blows up. So, for example, the Sharpe and Sortino ratios for the ETF MINT are absurdly high.

b) They rely on arithmetic rather than geometric measures of return. So funds that have lost a lot of money can still have positive Sharpe and Sortino ratios if their volatility is high, since the difference between arithmetic and geometric measures of return increases with volatility.

c) The ratios ignore the order of returns. A fund that gains 10% in a month, then loses 10% the next month, and so on for a year would have exactly the same Sharpe and Sortino ratios as a fund that gains 10% for six months straight and then loses 10% for six months straight. But the latter fund would have a drawdown over five times larger.

Beta, on the other hand, doesn’t measure volatility in the same way as the Sharpe and Sortino ratios. Instead it focuses on the difference between the fund’s return and the return of the benchmark. A beta close to 0 is going to have no return at all, a beta close to 1 will match the return of the benchmark, a beta higher than 1 will be more volatile than the benchmark but be in the generally the same direction, and a negative beta can be wildly volatile but uncorrelated with the benchmark. Measurement of beta suffers from some of the same flaws as the Sharpe and Sortino ratios, but its purpose is fundamentally different. It should not be mistaken for a straightforward volatility measure. For that, use the standard deviation. Or better yet, create an Excel spreadsheet that will allow you to use mean deviation, geometric measures, and prices rather than returns.

I think it’s very important to take volatility of returns into account, but finding the best way to do so is at best a work in progress. There’s a very simplistic shortcut that I use sometimes: take the CAGR and multiply it by 1 minus the maximum drawdown.

But in general, ALL measurements of past performance are misleading for ETFs. Look at GLD from 2006 to 2011. What a chart! Very little drawdown, great return, not much volatility. Now look at it since 2011. Horrors.

In conclusion, I’d advise you not to mix Sortino and beta–the results would probably be a real jumble.

  • Yuval

Incredibly detailed response. Thank you

Yuval’s example demonstrates the flaw in using historic risk metrics in a model that needs to pick for the future. On a security-specific level, the factors that can make for a very good Sortino and the exact same ones as can make for a very bad Sortino if things suddenly break badly. In stocks, all of these factors have to do with the inherent volatility of the business and whatever additional volatility is introduced by the company structure (fixed operating costs, fixed interest expense, internal diversification, etc.). In fixed income, maturity/duration will go a long way toward making volatility what it is.

In stocks modelling, quality factors are better to control for risk. ETFs are more challenging. To cut risk, you’d likely want to work with taxonomy inclusion/exclusion, no LT fixed income, no leverage, no emerging markets, etc.) Statistically, you’d want to focus on the symmetrical measures of variability, beta, and use a variety of measurement periods to increase the likelihood that the ETF has been reacting to the underlying characteristics of its holdings rather than to oddball events. Beta is better than StDev since it focuses more closely on the inherent characteristics of the portfolio (if used with enough time samples to minimize the risk of odd events) as opposed to amrket volatility (StDev) or even skillfull index construction (Sharpe).

Huh? Doesn’t beta represent the loading factor against systematic returns as represented by market/benchmark returns? With beta=0, there is still alpha to contribute to total returns. I hope that’s right, since I have a book with beta~=0 and and AR~=12%.

Best,
Walter

Sorry - it’s going to have the same return as the risk-free rate, which these days is very close to 0.

Nice save! :wink:

EDIT: but there’s still alpha. Right? At least, that’s how I think of beta/alpha and their significance.

Alpha combines the actual return with the beta in a more-or-less sensible way, but it’s not really a volatility-adjusted return like the Sharpe and Sortino ratios since a volatile negative beta will boost alpha above the actual return. My personal problem with using alpha is that SPY, by definition, has an alpha of 0, and it’s one of the best investments you can make. Even MINT, whose return is very close to 0, has a higher alpha than SPY.

With beta, the question is whether you prefer very low volatility (beta between 0 and 1), high volatility that’s correlated with the market (beta above 1), or volatility that’s uncorrelated with the market (beta below 0). Equity-based funds that significantly outperform the market tend to have high betas.

Quantopian wants models w/ Beta<=0.30 for their “hedge fund”. My zero beta book sims just fine, but it hasn’t run out of sample long enough to make any interesting observations. I think it may be severely tested this year.

Walter

Beta is used to compare the volatility of price movement to the risk of a single price series. That price series is usually the S&P 500 as a stand in for the market in general.

A beta of zero means that the stock that you’re examining has no relationship to the returns of the compared price series. So if a stock has a beta of zero against the S&P 500 then its price movement has no relationship to the movement of the S&P 500.

A beta of zero is most often found in other asset classes. The price of real estate (not a REIT stock, but actual land) is somewhere that I’d expect to see a beta of zero (or close to it).

This means, effectively, that an asset with a beta of zero has no market risk, or at least no risk related to market volatility. Don’t make the mistake of thinking that there’s no risk there, though. There’s likely to be some risk related to just being part of the economy, unless the asset is truly risk-free. (I’ve got a Venezuelan stock with a really low beta…) Non-equity asset classes have their own risk profiles.

In my ranking I was using the Sortino 2y/beta 3 and looking for higher ranks. My universe of ETFs was limited to sector ETFs, index ETFs and some fixed income.

I like this exampleof zero Beta: A beta can be zero simply because the correlation between that item’s returns and the market’s returns is zero. An example would be betting on horse racing. The correlation with the market will be zero, but it is certainly not a risk-free endeavor.

Another comment on beta is that a stock’s beta varies over time. It is best to probably use something less than 3 years. You can lookup a stock’s beta on websites and get all kinds of answers. you need to know what time-frame it is being measured over. P123 tells you what time frame it is derived from. You can also dial in your own using the beta function.

Technically, David and Paul are correct, but in practice, zero-beta ETFs tend to be very low volatility. Here’s a screen I ran of ETFs with a beta between -0.05 and 0.05.