diversify your portfolio to overcome variance drain
In the previous blog Portfolio volatility kills your compounding gains. Here’s why, we saw how portfolio volatility drains your compounded returns (CAGR). As an investor, CAGR is what matters to us.
In this blog, we will see how diversification can help us control volatility, which in turn, reduces the impact of variance drain.
We saw how Nifty 50 index, in the last 15 years, has delivered a CAGR of 10.8% despite having an average annual return of 15%. Gold, on the other hand delivered a CAGR of 11.1% with an average annual return was 12%.
The reason for this discrepancy was “variance drain”. Annual returns of Nifty 50 had a volatility of almost 30% while annual returns of gold exhibited just 14.3% volatility. Therefore, despite lower average return, gold delivered a better CAGR.
We also presented an approximate formula to capture the variance drain effect:
G ~ M – V2/2
Where G is the CAGR, M is the average return and V is the volatility of return.
As the formula shows, higher the volatility, lower will be the CAGR (with fixed M). Therefore, reducing volatility can reduce the impact of variance drain.
However, reducing portfolio volatility does not happen magically. If we attempt to reduce volatility, we must compromise on the expected return as well (M).
Therefore, reduction in portfolio volatility should be large enough to compensate for reduction in expected return such that overall CAGR increases as per formula above.
In our Nifty 50 and Gold example, as we moved from Nifty 50 to Gold, drop in average return was 3% but the drop in volatility was almost 15%. This compensated for the 3% drop and hence, the CAGR of gold was higher.
For the purpose of this blog, we will assume that readers are familiar with the concept of diversification.
Diversification, very simply put, is the practice of investing in multiple securities and/or multiple asset classes. Investing in multiple securities ensures security level diversification while investing in multiple asset classes ensures asset level diversification.
Also, for the sake of simplicity, we will continue with Nifty 50 and Gold as the only 2 asset classes (although the concept applies to multiple asset classes as well).
So far, we have looked at 2 extreme portfolios – 100% Nifty 50 and 100% Gold. Table below summarizes what we have learnt so far:
What happens when we create portfolios that are combinations of these 2 assets.
Table below shows 11 portfolios with Nifty 50 weight declining uniformly from 100% to 0%. All these portfolios are rebalanced quarterly.
The chart below provides a visual illustration of how average return (M) and CAGR (G) changes with different portfolio weights:
As we can see, average return (M) declines as we move from riskier asset (Nifty 50) to less risky asset (Gold). However, CAGR improves up to portfolio 6 (50% in both assets).
This is the power of diversification – despite reduction in average return, CAGR improves because reduction in volatility is even more.
Diversification helps us reduce portfolio volatility without compromising too much on the average return. Lower volatility can help investors achieve higher CAGR with lesser risk.
Few important points to note:
It should also be noted that we have deliberately chosen Gold as the diversifying asset because it clearly conveys the impact of diversification – CAGR improves significantly by diversifying. Instead of Gold, if we use Debt as the diversifying asset, there is no significant improvement in CAGR (over Nifty 50 CAGR) since return differential is large.
This does not mean that investors should not invest in Debt. CAGR improvement is just one positive byproduct of diversification, caused by reduced volatility. There are many other aspects of diversification which we have not covered in this blog.
Diversification math under the hood
We have not covered the underlying math behind diversification – what causes the reduced volatility? The math behind diversification is at the heart of Modern Portfolio Theory (MPT) and Mean Variance Optimization (MVO). Interested readers can check this link to explore the underlying math.
We will conduct a quick Monte Carlo experiment to demonstrate the power of diversification. Consider an asset A that has one-period expected return(M) of 4.5% and volatility (V) of 30%. These numbers are unrealistic but chosen deliberately to illustrate a point. Note that as per our variance drain formula for CAGR (G) [G ~ M – V2/2], expected CAGR of this asset is 0.
We generate 1000 30-year price paths (assuming Geometric Brownian Motion). As expected, average CAGR of this asset turns out to be roughly 0. Now we add another asset B that has same M and V and exhibits 0 correlation with A. We construct an equally weighted portfolio of these 2 assets, rebalanced annually.
30-CAGR of this portfolio becomes 2.3%! That’s the magic of diversification. This happens because portfolio volatility reduces from 30% to 21%. If you add another asset C which has 0 correlation with A and B and construct an equally weighted portfolio (rebalanced annually), CAGR further improves to 3.0%. Diversification has turned 0 CAGR assets into positive CAGR portfolios.
Chart below shows the CAGR of portfolios with increasing number of uncorrelated assets (x-axis):
As we can see, as we increase the number of assets, CAGR converges to one-period expected return (M).
Reduction in volatility follows a nice mathematical formula – V/sqrt(N). Where N is number of uncorrelated assets that have equal weights in the portfolio. Theoretically, if you have large number of uncorrelated assets, you can completely eliminate variance drain.
In reality, it is very difficult to find multiple assets with 0 correlation. But directionally, diversification still works even when assets exhibit positive correlation.
Throughout our analysis, we have assumed that all portfolios are rebalanced quarterly. Is rebalancing necessary? What happens if portfolios are not rebalanced? We explore these questions in our next blog.