Tag: mutual funds

Probabilistic Sharpe Ratio

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.

Probabilistic Sharpe Ratio

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.

Quant Model in Mutual Fund Wrapper

Most quant/smart-beta model based portfolios in India are built on direct-equity platforms – PMS, RIA, Themes and DIY. Their first major drawback is the 15% capital gains tax that needs to be paid the piper every year. The second one is the ability to track the “all-in” cost of maintaining the portfolio. This is where mutual funds have an advantage. Their pass-through status means that they don’t have to pay capital gains tax on portfolio sales and the end-of-day NAV gives investors the fully baked-in value of their portfolio. That said, mutual funds that wrap quantitative models have been few and far between. A new one has entered the fray: the DSP Quant Fund.

They were gracious enough to share their backtest. What follows is a 30,000 foot analysis.

Cumulative performance looks vs. a broad-market cap index looks good

cumulative performance vs. NIFTY 100 TR

However, excess returns seem to be tapering off…

excess returns over NIFTY 100 TR

Value factor seems to be a drag

If you regress the Quant Fund against the market-cap index and NIFTY strategy indices representing quality and value, you can see that returns have been primarily driven by the market (beta) and quality. Value seems to contribute negatively to overall returns. Part of the diminishing excess returns could be explained by the increasing influence of market beta to the fund’s returns.

drivers of returns

Why not just buy the NIFTY 200 Quality 30 Index Fund/ETF?

cumulative performance vs. NIFTY 200 Quality 30 TR

The SBI Quality ETF that tracks the NIFTY 200 Quality 30 Index has an expense ratio of 50bps. So while comparing the index against the Quant Fund, we need to haircut the index performance by that amount. Also, the Quant Fund comes out at 40bps for direct investors. The former is an ETF with minimal liquidity whereas the latter is an open-ended fund that can be redeemed at NAV – matters when you want to exit.

Qualitatively speaking…

DSP’s Quant Fund is a low-cost alternative to investors who want something more than market beta but not a full-fledged actively managed fund. It is tax efficient compared to other direct-equity platform solutions that over-weight the quality factor. And it is of comparable cost to most other quant/smart-beta funds/etfs for direct investors. Passive investors should definitely give it a strong look.

Code and charts are on github.

What is the right benchmark for funds owning US equities?

Some funds, the Parag Parikh Long Term Equity, for example, have a carve out for international (primarily US) equities. From a tax perspective, if a fund owns at least 65% of its portfolio in Indian stocks, it is treated as “Indian Equity Fund” for taxation – 15% short-term gains and 10% long-term gains (if held beyond one year). Otherwise, short-term gains (if held for less than 3-years) are added to your income and taxed at your marginal rate. So there is some advantage in packaging US stocks inside a an Indian equity fund. However, what is the appropriate benchmark in this case?

The PP-LTE Fund benchmarks against the NIFTY 500 TR index. But based on its portfolio, it should ideally be benchmarked against a 65/35 Indian Midcap/US Large Cap index. If you construct an Index with the M100 ETF making 65% of the portfolio and the rest allocated to the SPY ETF (tracking the S&P 500 index,) you will get an idea of the fund’s alpha/excess returns.

Parag Parikh Long Term Equity vs. 65/35 M100/SPY:

If you rebalance the 65/35 monthly, the LTE Fund’s annualized returns are 16.47% (Reg.) and 17.10% (Dir.) vs. the 65/35’s 15.30%. That’s excess returns of 1.8% for the direct plan, delivered to investors in a tax efficient manner, after all costs have been factored in. Another way to look at this is that even if the present management is replaced and investors do not have faith in the new one, they can just replace the fund with two ETFs and get almost to the same place.

Code and charts on github.

Fund Portfolios and Market Cap Deciles

When you sort the universe of stocks in descending order of their free-float market caps and divide them into 10 sets, you end up with StockViz Deciles. If you were to plot the dispersion of market-caps within deciles, here’s how it would look:

market cap deciles

Most of the activity in the markets are in the first 3-4 deciles. Liquidity, as measured by the bid/offer spread, trails off as the float drops:
bid/offer spread by market cap decile

The wide bid/offers presents a scale challenge to small-cap fund managers. The hair-cut to NAV that they will have to take while crossing the spread is just too large. So most small-cap funds pull up:

Notice how most of the portfolios is concentrated above the 4th decile. Now, contrast this to the NIFTY SMALLCAP 250 index:
SMALLCAP 250 overlap
If the funds were to stay true to their small-cap moniker, they really shouldn’t be holding decile 0 (mega-cap) stocks. However, holding them seems to be the only way to scale AUM.

If you care about whether a fund is sticking to its portfolio mandate, give our Overlap Tool a spin.

The Path Dependency of SIP Returns

Our previous post on Lumpsum vs. SIP returns showed how, given the way returns are statistically distributed, lumpsums tend to perform better than SIPs. The analysis side-stepped a lot of issues with using a single market-price time-series by fitting the weekly returns of the index into a Generalised Lambda Distribution and then using that model to run a simulation. This may not seem “real” to most investors. Even through the weekly returns obtained by querying the model is from the same distribution as that of the index, it may not reproduce the exact path that the index took. In this post, we will present a simpler analysis that should be more intuitive.

Random sampling

Most SIP/DCA investors setup a monthly purchase and let it run for a period of time. So we will mimic that process by using monthly returns for our analysis. Moreover, instead of building a statistical model, we will just randomly shuffle the observed set of monthly returns to obtain a return series for our simulation. Each simulation will then end up having the same monthly returns but in a different (random) order. We then calculate SIP/DCA returns for each of those and plot them as a histogram.


Here is how NIFTY 50’s randomized monthly SIP/DCA looks like:
NIFTY 50.monthly sip random shuffle
What the above chart means is that both SIP/DCA and lumpsum actual returns are path dependent. A re-ordering of the same monthly returns end up giving vastly different results. This also shows why even if a particular investment gives superior returns, individual investors can still end up with poor returns because of path dependency.

Below are the charts for MIDCAP and SMALLCAP indices:
NIFTY MIDCAP 100.monthly sip random shuffle
NIFTY SMLCAP 100 monthly sip random shuffle

*Key assumption here is that monthly returns are randomly distributed. But trend-followers would disagree on that point.

Code is on github.