Tag: backtest

Momentum Rebalance Frequency

Previously, we found that the traditional 12_1 momentum configuration, where you look at the previous 12-month performance while skipping the most recent month and rebalancing every month, was indeed an ideal config (MOM_1_1). However, there are momentum index funds that rebalance once in 6-months (MOM_[0,1]_6). Is there any performance give-up if you rebalance infrequently?

Turns out that the traditional config is quantifiably better than others. However, there’s isn’t much of a performance give-up even if you rebalance once in 6-months (MOM_0_6).

Besides, the analysis here doesn’t factor in transaction costs which would be a bigger drag on the monthly rebalance config. When you add the tax-advantage and low-cost of index funds into the mix, the current crop of momentum index funds don’t look all that shabby.

Code and charts on github.

Momentum Skip Month

The original Jegadeesh and Titman momentum paper (pdf) used a “skip month” to manage the reversal effect (quant.stackexchange). However, why is it one month and not two, or three or four?

Here’s what the equity curves of different skip month configs look like.

The “skip one month” is indeed a magical config. Also, if you are optimizing for Sharpe, skip two.

Code and charts on github.

Volatility, Volatility of Volatility, and Momentum

Momentum has proved to be the premier anomaly in different markets. And so has low-volatility. What happens if you combine both of them? Also, what if you also add low volatility of volatility into the mix?

There are a couple of ways to skin this cat. You can start with low-volatility and add momentum. Or, you could go the other way – start with momentum and then add a volatility sort.

tl;dr: go with low-volatility first, momentum second (VOLxMOM).

While a simple momentum sort gives the highest return, adding a low-volatility filter to it gets you a better risk-adjusted return.

The order of the sort – first volatility and then momentum or first momentum and then volatility – doesn’t seem to matter much for the Sharpe rankings but the former ended up with slightly better returns.

Code and charts on github.

Cross-Asset Time-series Momentum

Trend-following systems typically use the past performance of a particular asset to trigger a buy or a sell on that asset. A research paper that came out in 2019 looked at whether the historical performance of multiple assets can be used to trade them.

Pitkäjärvi, Aleksi and Suominen, Matti and Vaittinen, Lauri Tapani, Cross-Asset Signals and Time Series Momentum (January 6, 2019). Available at SSRN: https://ssrn.com/abstract=2891434

From the abstract:

We document a new phenomenon in bond and equity markets that we call cross-asset time series momentum. Using data from 20 countries, we show that past bond market returns are positive predictors of future equity market returns, and past equity market returns are negative predictors of future bond market returns.

Unfortunately, the paper did not look at Indian markets to check if this worked. So, we rigged up a simple backtest to see for ourselves.

Rules

A simplified equity-bond cross-asset trading strategy at the beginning of month t can be constructed as follows: Compute the past 12-month equity return (E past) and the past 12-month bond return (B past). If:

a) E past is positive and B past is positive: Buy equity
b) E past is negative and B past is negative: Sell equity
c) E past is negative and B past is positive: Buy bonds
d) E past is positive and B past is negative: Sell bonds
e) Otherwise, invest in the risk-free rate.
Hold the portfolio for one month and then repeat the same procedure in month t+1 (source.)

Backtest

We used the NIFTY 50 TR index to represent equities, NIFTY GS 10YR index for bonds and the CCIL Index 0-5 TRI for risk-free rate.

Since our risk-free index starts only from 2004, our backtest only goes back 16 years. However, the markets have been through a lot since then, so it is unlikely we are losing much by not being able to go back much earlier.

The 12-month look-back approach massively under-performs the NIFTY 50 TR buy-and-hold. We shortened the look-back to 3-months to see if we could make the strategy more responsive to trend reversals.

To our dismay, we saw only marginal improvements in overall returns but the draw-down profile of the long-only portfolio was much better.

Conclusion

While the approach outlined in the paper might be valid for the selected subset of markets, it fails a simple backtest on Indian market indices.

Code for the backtest can be found on github.

Risk Management is Not Free

Now that we are in the middle of a massive virus induced selloff, investors are once again interested in risk management. Similar to how flood insurance is mostly bought after a flood, investors end up paying a hefty premium for fighting the last war. Our experience with offering strategies that try to manage downside risk has been that investors flock to it after a drawdown, only to get disappointed by its returns once the market recovers and getting rid of it right before the next one. Rinse, Repeat.

Risk management is not free

No matter how you hedge your risk (buying options, sell futures, trend-following,) it costs money. There is no system where risk management makes the investor money. So, by definition, hedged investment returns will trail buy-and-hold for long periods of time.

Drawdowns and Returns are sides of the same coin

Equity risk premium exists because of tail-risk that cannot be modeled.

Nothing “normal” about it!

No matter what your time-horizon, there are always periods when you will be deeply in a hole.

Hedging instruments are not perpetual

Equities are perpetual but hedging instruments like futures and options have definite terms. They have their own peculiarities based on risk that is already being priced in vs. true tails.

Simple Moving Averages can help

Being long an index only when it above an SMA is one way to overcome the problems highlighted above. It doesn’t involve hedging instruments, so you don’t have to worry about derivative pricing, expiry, etc. The odds are in your favor in terms of the trend being your friend.

On average, it pays to be long only when the NIFTY is above its 50-day SMA

Most of the large daily moves occur when the index is below the SMA. Higher volatility is not necessarily bad if the drift is higher. But most investors rather sit out the volatility than dive in get their guts punched.

Next-day returns under different SMA “regimes”

What would returns look like if you were long only when the index traded above its SMA? It really depends on your time horizon.

Including the 2008 GFC
Excluding 2008 and subsequent recovery
Annual returns
Get ready to be whip-lashed
Trade-off between lower volatility and higher costs/gross returns.

Problems

  • When it comes to avoiding drawdowns, you win some, you lose some.
  • Transaction costs matter. The above was modeled using an STT of 0.001% and slippage of 0.05% on the sell side. And capital gains taxes have been ignored.
  • Trading this using ETFs would be sub-optimal. So it is not clear how this strategy can be expressed.
  • Outcomes would depend on holding periods. Investors can go a long time under-performing the index and experiencing every bump that comes along.
  • Shorter the SMA period (50-day shown above is not written in stone,) more the transaction costs and slippage.

Different look-back periods

What if you shortened the SMA period to 20 days?

20-days

And what if you increased it to 200 days?

200-days

What about Midcaps?

20-days
50-days
100-days
200-days

Who should hedge?

Most of the time, markets recover. However, the recovery time varies each time and there is no way to time hedging strategies. And each under-lying index behaves differently.

So, the reason to do it is investor’s own psychology and the asset one is long. If you, as a buy-and-hold long-term investor, can stomach the volatility, then there is probably no reason to hedge. Besides, portfolio volatility can be reduced through asset allocation as well (here, here.)

And remember: risk-management, whatever the strategy, involves paying upfront to mitigate risk that may or may-not befall.

Code and more charts on github.