Author: shyam

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.

90 days of Minimum Volatility

We had discussed portfolios optimized for minimum volatility back in January (see: Low Volatility: Stock vs. Portfolio) and had setup Themes that track such strategies. Broadly, these fall into ETL (Expected Tail Loss) and Min-Var (Minimum Variance) optimized portfolios that either take in the entire universe of stocks or only those that have a high momentum score. So, we have Minimum Expected Tail Loss, Minimum Variance, Momentum (Min-ETL) and Momentum (Min-Variance).

We expect optimized portfolios of momentum stocks to perform better during market up-trends. During bears, we expect them to have lower drawdowns than the market. The Corona Virus Panic put these portfolios in through the wringer. Glad to report that they came out largely unscathed.

Minimum Volatility Portfolios vs. NIFTY 50

Our back-tests showed that optimized momentum portfolio would under-perform “raw” momentum during up-trends but should have lower drawdowns during down-trends.

Momentum: Optimized vs. raw

Optimized momentum portfolios saved the investor about 3-4% in drawdowns compared to the “raw” momentum portfolio. May not sound like much in this instance but think about the cumulative effect over multiple market corrections when you invest for the long-term.

Overall, optimized portfolios delivered what they promised.

WhatsApp us at +91-80-26650232 if you are interested in knowing more about these strategies.

90 days of Factor Momentum

Last Decemeber, we had presented a back-test of a factor rotation strategy that would go long the factor portfolio that performed best over a look back period. The Themes based on this backtest have finally completed 90 days in the market. Here’s a quick update on their performance.

Indian Factor Momentum

We went with two flavors here. One that went long a portfolio of stocks in NSE’s strategy indices – Factor Momentum (Indices) – and another that went long one of our factor portfolios – Factor Momentum (Themes).

Factor Momentum (Indices)

Factor Momentum (Indices) performance after brokerage and STT

Factor Momentum (Themes)

Factor Momentum (Themes) performance after brokerage and STT

Thoughts on Performance

Both portfolios crashed as much as the large and midcap indices during the Corona Virus Panic. However, it appears that the recovery from the crash has been lead the Index variant. For a while, it did look like the Theme variant out-performed the indices but it may have been because of the randomness introduced by the smaller number of stocks in the portfolio.

US Factor Momentum

Factor Momentum III

The US context is wildly different from India. With brokerage costs at zero and with the ability to trade fractional shares, the portfolio can be efficiently rebalanced with a one-month look-back (Factor Momentum III.) Given the steepness of the fall during the Corona Virus Panic, the shorter lookback helped it quickly adjust to the market and keep drawdowns to less than 10% compared to SPY’s 30%+

WhatsApp us at +91-80-26650232 if you are interested in knowing more about these strategies.

Risk Management is Not Free, Part III: Hedging

We often hear about portfolio hedging – how you can short NIFTY futures or buy puts – to reduce portfolio losses. The chapter, Hedging with Futures on Varsity, is a good introduction to the mechanics involved. However, real life involves tradeoffs.

How much to hedge?

This one is pretty straightforward. A fully hedged portfolio means that your total returns are driven purely by excess returns. Given that excess returns are typically not more than 5%, it may not make sense for most investors. So, most do a partial hedge. And a partial hedge means that when volatility strikes, you are still exposed to downside risks.

The other problem with hedges is that most investors think of risk in terms of absolute draw-downs (not volatility.) i.e., “My portfolio is down 15%,” not “My portfolio lost half of what the market lost.” So hedging first requires a change in how investors perceive risk.

Portfolio betas are not invariant

Suppose you want to be long quality stocks but want to hedge part of the portfolio by shorting the NIFTY, then how do you go about calculating the portfolio’s beta? Your assumptions of the risk-free rate and the look-back period will greatly influence the final value. Also, beta is not a static number that you can assume and keep unchanged through time.

1-year beta
3-year beta

Hedging costs increase with volatility

Volatility is huge part of derivative pricing. When you trade futures, you have to post margin to your broker and options have an implied volatility baked into their premiums. So irrespective of how you choose to hedge your portfolio, you will find that when volatility arrives, hedging costs increase.

For example, the margin requirement for a single lot of NIFTY futures in late December was roughly Rs. 1,05,000/- With NIFTY ~12,100, that is roughly 11.5% of notional. But now, because of the virus induced spike in volatility, the margin requirement has gone up to about Rs. 1,50,000/- with NIFTY ~8250, or 24.25% of notional.

So, when you want your portfolio to be hedged the most, the cost of doing so has more than doubled. To fund this, you now have to choose between reducing the hedge ratio (and taking on more market risk) and liquidating the long-side of the portfolio to the extent of the deficit (while selling in a down market.)


There are no simple answers and each investor needs to arrive at these trade-offs based on their risk perception and tolerance.

Please read Part I and Part II of this series.

Risk Management is Not Free, Part II

The first part of this series discussed how SMA strategies can help manage draw-down risk while investing in indices. However, index investing doesn’t cover the whole breadth of strategies that investors typically run. Managing risk in a portfolio of stocks is quite different from managing risk on an index as a whole. One of the most basic strategies one can employ on a portfolio is that of a trailing stop loss on component stocks.

Trailing Stop Loss

In a TSL, a high watermark is tracked from the purchase price and an exit is triggered if the price falls below a certain percentage from it. You can read more about the mechanics here.

Some of the things that need to be thought through when using a TSL on a portfolio of stocks:

  1. What is the exit criteria? Should it be 5%, 10%… 15%? If you set it to low then you end up trading a lot; too high, and it may not make a difference.
  2. What is the re-entry criteria? Suppose you exit a stock today but it still checks all the boxes for inclusion in the portfolio, will you re-purchase it tomorrow?
  3. Are you going to replace an exited stock with another one that fits the inclusion criteria or are you going to hold cash?

A TSL only considers price to decide on an exit. So the most obvious place to apply it is in momentum portfolios.


Momentum stocks are prone to cliff risk. Back in 2016, we setup a momentum portfolio that has a 5% TSL on each of its components to see if we can reduce the severity of drawdowns of our more basic Momentum strategy. We called it Momo 1.1. Here are the cumulative returns and drawdowns of Static and Momo strategies, with and without considering transaction costs:

Momentum: Static vs. Momo

The red line is Static Momentum and the blue line is the Momo version of it, after considering an STT of 0.1% and brokerage of 0.05%.

As you can see, the after-cost returns of Momo trailed that of Static’s for quite some time. If you are a regular investor who has to pay capital gains tax (not someone who’s main business is stock trading,) then it is really painful to watch most of the notional gains evaporate into taxes.

This is because Risk Management Is Not Free. It involves trading off near-term profit to reduce potential risk in the future.

It took the sudden plunge in equities this year to bring out the value of having a risk-management process in place. The after-cost, annualized returns of Momo, since late June 2016, comes in at 17.54% while that of Static’s is at 9.5%. Moreover, because of the dynamic nature of Momo, it is currently 75% in cash, while Static is 100% in stocks.

Momo on US stocks

In early 2018, we ported the Momo strategy discussed above to US stocks.

Momo: US stocks

Once again, we see trailing stop losses saving our hides and, more importantly, preserving our returns. Momo comes in at an annualized 8.30% vs. S&P 500’s -6.08% during the same period. Its portfolio is currently 75% in cash. At zero brokerage and no STT in the US, you pretty much get to eat all of those returns.

Investment Horizon

When we looked at the performance of Momo back in May 2019, we had concluded that, maybe, investors were better off with the Static version (see Part I, Part II.) We had traced the subsequent performance of stocks that were thrown out because of a stop loss and had found that:

During the bull phase, when the whole market was shooting higher, stop-lossed positions recovered from their losses.

During the bear phase, it does look like stop-losses helped – the subsequent returns of stop-lossed positions were skewed left.

However, in aggregate, they did not add value after taking costs into account.

It boils down to the kind of risk you are trying to avoid and the time-horizon involved. If we were to add subsequent performance of these strategies to the above data-set, we may have reached a different conclusion.


  1. Risk management is not free. You pay upfront to mitigate risks in the future that may not befall.
  2. It is not always obvious if the risk management strategy is “working” and whether is is “worth it.”
  3. It makes sense to add a trailing stop loss to the components of a momentum portfolio given the high cliff risk of the strategy. However, the timing of these cliffs cannot be predicted.
  4. Taxes form a large chunk of costs when using a TSL based risk-management strategy.