Is Your Portfolio Diversified? No, it’s not. Maybe that’s best.

Posted on March 2nd, 2014 by admin in Portfolio Diversification, Quant

Harry Markowitz changed the investment world forever with his Ph.D. thesis in 1952. He showed how you can reduce portfolio risk by including stocks that have low or negative correlation with the ones already chosen. That lets you keep your expected return the same with less volatility of returns. Thus the old adage “diversification is the only free lunch”.

While his theory is valid it does have a well-known catch, which is rarely addressed by retail investors or their advisors: the theory applies for a fixed time period. But real investments are made for many time periods, or one very long time period, thus making it quite difficult to apply his ideas, especially concerning diversification. So if you create a well diversified portfolio, it can change to a very non-diversified one while you’re not watching. This observation, which we will support below, raises the question as to how often to rebalance your portfolio to ensure diversification. With monthly changes in correlations, it would seem that’s the frequency to adopt.

To demonstrate some of the difficulties of diversification we’ve constructed two portfolios to demonstrate some of the key ideas. We use the wonderful financial web service

www.Stockrover.com

to get the computation of stock standard deviation (“volatility”) per stock, returns over the time period per stock, and the correlation matrix among portfolio entities for each time interval. We then scale the annual standard deviation to account for time intervals of different length.

First, we make a portfolio of the stocks in our RIPSI index as modified. The firms all have similar business models and sell mainly to the electronics industry, so we’d expect to find this portfolio not diversified. Figure 1 shows this is a correct expectation.

Figure 1: Correlation matrix for equities in RIPSI for daily returns over the year ending on 2/21/14. Correlations vary from -1 (blue) to +1 (red). "Uncorrelated" is technically 0, and the user needs to decide how much bigger or smaller is an acceptable approximation.

Figure 1: Correlation matrix for equities in RIPSI for daily returns over the year ending on 2/21/14. Correlations vary from -1 (blue) to +1 (red). “Uncorrelated” is technically 0, and the user needs to decide how much bigger or smaller is an acceptable approximation.

 

The amount of dark cells shows high correlations dominate. This is natural, given how closely related all the businesses are in the IP industry.The main diagonal in Figure 1, which has all values of 1.0, separates the matrix into two triangles of correlations, and upper tight and a lower left. These are of course symmetric since correlation(x,y)=correlation(y,x). So if we consider only one triangle, say the upper, we can calculate the average correlation of returns among all the pairs of different stocks. We do this for each time interval of 1, 3, 6, 12, 24 months, each ending on the date 2-21-14. Figure 2 shows clearly these average values change substantially over each period.  So rebalancing is hardly stable.

Figure 3 shows how dramatically portfolio return vs risk varies as the measurement horizon varies. Figure 3 also shows a true anomaly. Since we expect returns to increase only with increased volatility, it’s a stark reminder of the time varying nature of the stock values that the return for 6 month lag is lower than for 3 months, but has higher risk.

Figure 3:

Figure 2: Matrix has substantial variation in correlations depending on length of time interval.

Portfolio Return vs Portfolio Standard Deviation, over time periods ending on 2-21-14.

Figure 3: Portfolio Return vs Portfolio Standard Deviation, over time periods ending on 2-21-14

 

 

 

 

 

 

 

 

 

 

Now consider a portfolio of apparently well diversified stocks. This alternative portfolio consists of ETFs that represent the standard sectors of the economy and a few other securities that seem very uncorrelated from the sectors.

The Standard Sector Portfolio consists of the ETFs and Indexes shown in Table 1.

Table 1: Portfolio of Standard Economic Sectors and Indexes

Ticker Index
GLD SPDR Gold Trust
GSG GSCI Commodity-Indexed Trust Fund
IYZ Dow Jones U.S. Telecommunications Index Fund
PTTDX PIMCO Total Return D
RWR SPDR DJ Wilshire REIT ETF
SPY SPDR S&P 500
TIP Barclays TIPS Bond Fund
XLE Energy Select Sector SPDR
XLF Financial Select Sector SPDR
XLI Industrial Select Sector SPDR
XLK Technology Select Sector SPDR
XLU Utilities Select Sector SPDR
XLV Health Care Select Sector SPDR
XLY Consumer Discretionary Select Sector SPDR

 

The correlation matrix for this portfolio is shown in Figure 4:

Figure 4: Correlation Matrix for Standard Sectors Portfolio, for 1 year horizon ending 2-21-14.

Figure 4: Correlation Matrix for Standard Sectors Portfolio, for 1 year horizon ending 2-21-14.

 

We compute the average correlations and Return vs Standard Deviation as for the RIPSI index above:

Figure 5: Significant variation is average correlation over time

Figure 5: Significant variation is average correlation over time

Figure 6: Portfolio Returns vs Portfolio Standard Deviation for Standard Sectors

Figure 6: Portfolio Returns vs Portfolio Standard Deviation for Standard Sectors

 

 

 

 

 

 

 

 

 

 

Again the variation in average correlation shown in Figure 5 is not smooth.  Figure 6 reveals that returns did follow risk monotonically for the standard sectors.

Finally, let’s directly compare RIPSI and Sectors. We consider Table 2 and Table 3:

FIgure 4: Summary of RIPSI Performance

Table 2: Summary of RIPSI Performance

Summary Sectors 2-21-14

Table 3: Summary of Sector Performance

 

 

 

 

 

For every time horizon, we see that  RIPSI has higher volatility (risk) than Sectors, and  smaller return over the horizon. We also see that the average correlation of the RIPSI portfolio is lower for each horizon.

Thus, RIPSI as a portfolio is more diversified, but also riskier, with worse returns than Sectors.

The take-away: diversification is good, but must be carefully constructed, and correlation time intervals must be watched to enable rebalancing frequently enough.

 

 

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