Author: shyam

Mitigating Sequence Risk through Asset Allocation

Sequence Risk (sometimes called sequence-of-returns risk) is the effect that the order of returns has on a portfolio.

For example, say you look at NIFTY and find that it gave negative 10% returns 4 years out of 10, and the rest of the years it gave positive 10% returns. You want to be invested for 5 years, so you expect 2 of those years to be negative. Sequence risk means that it is possible that you could have all of those negative 4 years during the 5 year period that you have invested.

The order in which losses occur impacts the portfolio’s terminal value

The annualized return of the NIFTY 50 TR index, since inception through May-2020, is roughly 12%. However, it has not been without periods where it was down over 50%.

NIFY 50 TR cumulative returns since inception

The lower part of the chart shows the drawdowns that have occurred in the past. Sometimes, it has taken years to recover from losses. The problem is that most investors have a pre-defined time-frame in mind. They want to be invested, say, for 10 years. Not “forever.” This is where sequence risk becomes a problem.

For a 10-year period, if you re-sample the monthly returns of the NIFTY 50 TR index and re-construct a return time-series, say, a 100 times, and plot the cumulative returns of each, it looks something like this:

The blue line is the “average” monthly return compounded for 10-years

Put another way, there is a non-trivial chance that an investor could end up with negative returns in a given 10-year period even if NIFTY’s return distribution did not change.

So, what is an investor to do? There are two approaches that have known to work:

  1. Diversification. Allocate to non-correlated assets.
  2. Get Tactical. Markets are known to trend. Try and preemptively exit from assets who’s prices are trending down.

There are a million different ways to skin each of these approaches. The simplest one is to add bonds to the portfolio.

NIFTY 50 TR and 0-5yr TRI

Bonds, especially sovereign bonds (issued by stable countries, of course) have very low drawdowns. So when you combine it with equities, you end up with a lot less sequence risk than pure equities.

If you simulate different proportions of equities and bonds and plot them along with their standard deviations, you’ll get an idea of where to trade-off stability with returns.

Trade-off between risk and returns

Let’s say that the sweet-spot is equity/bond ratios with avg. returns more than 10% but lower-bounded at 7.5%, you get 45/55, 50/50 and 55/45 as ideal allocations. While a 60/40 equity/bond allocation is the go-to for most advisors, there is no reason why it can’t be a more conservative 45/55.

Cumulative returns of different allocation ratios

Note the lower drawdowns of diversified portfolios. While the equity-only portfolio would have had an annualized return of 11.88% during the period, diversified portfolios ranged from 10.10% – 10.56%. The trade-off is that diversified portfolios have vastly less sequence risk.

The left-tail has been flattened while returns are now clustered more towards the average

Diversification changes the shape of the return distribution so that an average investor has a greater probability of experiencing average returns.

Read more about portfolio allocation across different assets here.

Code and images are on github.

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.)

Take-away

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.