Author: shyam

Our previous post showed how various allocation decisions impact an equal-weighted three-asset portfolio. However, equal-weights are not the only way to go. Every time a rebalance occurs, we can use that opportunity to re-weight the assets to minimize expected risk while maximizing expected returns. In this post, we look at two ways in which risk and returns can be optimized.

Portfolio optimization and the efficient frontier

The intuition behind what we are going to do is quite simple: for a given set of assets, there is an ideal mix of them that perfectly balances risk with reward. Imagine a plot of risk and returns of each asset under consideration. Harry Markowitz showed back in the 1950’s that they form a parabola and at a particular tangent of the parabola lies the ideal mix. The goal of portfolio optimization is to find that point. Here are some links that explain this concept further:

• investopedia.com
• wikipedia
• moneychimp.com
• yale.edu

For the purpose of this post, we will assume risk to either mean variance (var) or expected tail loss (ETL.) We will use portfolio optimization methods to minimize one of these risk metric and maximize expected mean returns below.

Optimized portfolios

Like before, to keep things simple, we will go with the MIDCAP 100 index (A1), the 0-5yr TRI (A2) and the QQQ ETF (prices converted to INR, A3) as the three assets that form our portfolio.

Here is how the optimized minimum-variance portfolio performs after-tax:

Asset weights after rebalance:

And here is how the optimized minimum-ETL portfolio performs after-tax:

Asset weights after rebalance:

Take-away

1. All things equal, the optimized portfolios under-perform the equal-weight portfolio in terms of absolute returns.
2. Optimized portfolios show lesser risk than the equal-weight portfolio. During the 2008 carnage, for example, equal-weight drew-down ~40% whereas optimized portfolios drew-down ~20%.
3. Optimized portfolios over-weigh bonds. Hard limits were set on the maximum and minimum weights the assets can have in optimized portfolios. Toggling these will have a significant impact on portfolio risk and returns.

Code, charts and the complete result dataset are available on github.

Our previous post showed how various allocation decisions impact a two-asset portfolio. We started with two assets – equities and bonds – because it forms the foundation on which most allocation plans are built. However, the true impact of diversification is felt when you have uncorrelated assets in the portfolio. Here, we expand on the post by adding a third asset.

Picking the Assets and Allocation

As much as we would like equities and bonds to be uncorrelated, it is not always true. Indian equities and bonds are buffeted by the same storms at about the same time. However, what has historically shown to be a true diversifier are international equities. If you run the pair-wise correlations between the S&P 500, Nasdaq 100, the USD adjusted MIDCAP 100 and 0-5yr TRI, you see this:

Given how strongly the S&P 500 (the SPY ETF) and the Nasdaq 100 (the QQQ ETF) are correlated, there is no point in adding both. We’ll go with the QQQ because it has an Indian analogue in the N100 ETF. Also, note how the SPY and QQQ are uncorrelated to the dollar adjusted MIDCAP and 0-5yr TRI indices. And finally, observe the light correlation between the MIDCAP and 0-5yr TRI indices.

So, to keep things simple, we will go with the MIDCAP 100 index, the 0-5yr TRI and the QQQ ETF (prices converted to INR) as the three assets that form our portfolio. And to get things started, we’ll keep an equal weight on all these three assets in the portfolio. The toggles that remain are the rebalance thresholds and tax impact. Here, we will use the same iterations that we employed in our two-asset portfolio example.

The results

In the cumulative return and drawdown chart below, A1 is the MIDCAP index, A2 is the 0-5yr bond index and A3 is the QQQ. A tax drag of 10% and an STT of 0.1% is applied at every rebalance. The rebalance threshold is set at 20%. The blue line is the resulting equal weight 3-asset portfolio returns.

Take-away

1. Lower risk: The equal-weight portfolio draws-down less than the MIDCAP index.
2. Lower returns: The MIDCAP index out-performs the equal-weight portfolio (but with far greater volatility.)
3. Needs discipline: The difference in returns between the MIDCAP index and the equal-weight portfolio can often be very large. Keeping still is a virtue.
4. Tax-impact: The equal-weight portfolio has a tax and transaction cost angle that a MIDCAP buy-and-hold strategy doesn’t. Capital gains on international equities, bonds and domestic equities are all treated differently.
5. Asset allocation is about delivering better risk-adjusted returns through diversification.

Side note: setting the rebalance threshold is a trade-off between holding onto trending assets (potentially more profits) vs. booking profits and buying a lower-return asset (FOMO and tax incidence.) There is a wide range of theories on this topic. For now, we will restrict ourselves to just running through different scenarios.

Code, charts and the complete result dataset are available on github.