Tag: mutual funds

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.

Mutual fund portfolio overlap in UpSet charts

Mutual funds come in different shapes and sizes. Very often, fund investors end up being exposed to the same set of stocks even if they invest in different funds. And not only can there be significant overlap in mutual fund portfolios, some fund managers could be “hugging” the benchmark index. For example, a mid-cap fund could have too much of an overlap with the mid-cap index, effectively making it a more expensive version of an index fund. Therefore, it makes sense for investors to check the portfolio overlap of funds that they are considering not only with each other but also with index constituents.

A common way to visualize overlaps is with a Venn diagram. However, when you have more than five sets (portfolios,) a Venn diagram becomes hard to read. Enter UpSet charts. Here is an UpSet chart that our Overlap Tool creates for the HDFC Mid-Cap Opportunities Fund and SBI Magnum Mid-Cap Fund portfolios:
HDFC Mid-Cap Opportunities Fund and SBI Magnum Mid-Cap Fund portfolio upset chart

Key regions of the chart:

  • Bottom-left: size of each portfolio.
  • Bottom-right: the intersection under consideration.
  • Top-right: the size of the intersection.
  • Titles: Funds being analyzed and their portfolio disclosure dates.

In this example, to see the overlap between the two funds, search for the connection between the 1st and the 4th rows in the bottom-right region and look up – you will see the size of the intersection to be 4. i.e., the funds only have four stocks in common even through each one has more than 50 stocks in its portfolio.

We have included some common indices to help investors identify index-hugging as well. You can run the Overlap Tool here. For an intro to the other tools available on StockViz Tools, please read this post.

Mutual Funds: A quick note on performance metrics

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.

We take a 200-week sliding window of midcap mutual fund returns and calculate its alpha, beta and information ratio. Here’s how these numbers stack up for the HDFC Mid-Cap Opportunities Fund.
HDFC Midcap fund

What is apparent here is that

  1. There is no case for dropping a fund because of declining alpha. Alpha keeps changing through time.
  2. You cannot escape negative beta.
  3. Managers seem to be able to outperform on the way up but not under-perform drastically on the way down. This is asymmetric risk/reward for those who can stick with investments through long periods of time.
  4. Some argue that recent SEBI regulations on mutual fund holdings will erode alpha. Only time will tell if that is true because of (1) and (2).
  5. Under-performance is not permanent. See ICICI’s fund below.

ICICI midcap mutual fund

What we see here is that at least in the midcap space, funds have been able to outperform the index in the past (both recent and distant.) However, that is no guide to the future.


  • The total-return index doesn’t go back long enough to be used for this analysis.
  • The risk-free rate used was the 0-5 year YTM adjusted for the weekly time-series.

Code, charts and time-series alpha, beta and IR for about a dozen mutual funds that are over 10-years old are on github.