Tag: mutual funds

In our introduction to factors, we discussed how portfolio returns are mostly explained by market risk (r_m – r_f: market risk premium.) Whatever cannot be explained by the market is α, or the portfolio manager’s skill. If you strip away the financial jargon, this is nothing but linear regression.

Also, what exactly is “market risk?” A few years ago, the only index funds on the market were of the NIFTY 50 and MIDCAP 150 indices. However, the number of index funds keep ticking up and there are now several strategy funds covering quality, value, low-volatility, momentum, etc… in the market. So, if an investor can access these vanilla strategies at a low cost, shouldn’t the definition of the “market” expand to incorporate those?

For example, take the HDFC Mid-cap Opp. Fund. You could regress its returns against the NIFTY MIDCAP 150, the NIFTY MIDCAP150 QUALITY 50 and NIFTY500 VALUE 50 indices to get an idea of how its α over them has evolved over time.

Rolling regressions gives you an idea of portfolio tilts and the fluctuating nature of α (Ax100). Also, its worth noting that α is only tangentially related to excess returns (XS). There are periods here where XS was positive in spite of negative Ax100 and vice versa.

Styles go in-and-out of favor. Sometimes Quality performs better than Value and sometimes a simple cap-weighted index will outperform everything else. An actively managed portfolio’s relative performance to these styles change over time as well.

tl;dr:

• α is a statistical derivation.
• Don’t go chasing α – it keeps fluctuating.
• α is not the same as excess returns.
• When in doubt, index and forget.
• You are always in doubt.

We have setup a script that auto-updates every day with these regressions on select large-cap and mid-cap funds. The report is available here.

There is absolutely zero stability in metrics used to analyze mutual fund performance. Whether it is alpha, beta or information ratio, they all vary over time and across market environments. Using them to pick the next “winning” fund is pointless. They are, at best, a measure of what happened in the past.

Mutual Funds: A quick note on performance metrics

Sharpe Ratio was one of the first attempts at quantifying investment returns. It is simply the average return divided by the standard deviation of returns. However, the approximation that returns are normally distributed makes it unsuitable for comparing across different investments/strategies.

But what if you kept the basic assumption that returns are normally distributed and introduced adjustments for kurtosis and skewness? One such approach is Marcos López de Prado’s Probabilistic Sharpe Ratio (pdf.)

Let’s say the calculated (historical) Sharpe Ratio of the investment is SR^. The benchmark has a Sharpe of SR*. Then, the Probabilistic Sharpe Ratio, PSR(SR*) = Prob[SR <= SR^]

Intuitively, PSR increases as the standard deviation of SR decreases, increases with positively skewed returns and decreases with fatter tails.

So, given investments with similar Sharpe Ratios, invest in the one that has a higher PSR.

We took two large-cap mutual funds that have been around since 2006, the NIFTY 50 TR index and a basic SMA-50 long-only strategy over NIFTY 50 TR to see how the ratios shake out.

From what we see here, both from a historical Sharpe as well as PSR, given a choice between MF1 and MF2, one would pick MF1.

Our take: PSR is valuable in cases where you have to choose between multiple strategies with equally attractive Sharpe Ratios since it gives a confidence level around that number.