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

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

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.

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.

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:

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

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:

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.