USMV: One Problem With Equating Historical Volatility And Risk

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PSA is the top holding in USMV because it currently exhibits low correlations with other stocks.

PSA requires external funding to sustain its dividend growth rate and high valuation.

PSA should become highly correlated with other stocks and underperform the market when external funding is expensive.

The risk models underlying USMV are blind to the funding issue and underestimate the risk of PSA.

USMV exemplifies one problem with statistical risk models.

By Bill Wynne

In my previous article, I described and analyzed the construction methodology for the iShares MSCI USA Minimum Volatility ETF (NYSEARCA:USMV). This article will demonstrate one problem with relying on historical volatility as the sole measure of risk. It starts with the following anomaly: Public Storage (NYSE:PSA) is the top holding of USMV. This occurs because PSA has recently exhibited low correlations with other stocks. However, PSA requires external funding to grow its dividend and support its current valuation. If attractive funding is unavailable, it should become highly correlated with other stocks and underperform the market. Since MSCI forecasts volatilities and correlations based upon recent historical data, their models are blind to this possibility and underestimate risk. Consequently, USMV allocates too much weight to PSA and exemplifies a significant problem with using statistical risk models for portfolio construction.

PSA is the top holding of USMV because of its low correlations with other stocks

Figure 1 depicts the top holdings of USMV by weight as of 4/5/2016. Source: Blackrock

Minimum volatility strategies may select holdings based upon data anomalies. Figure 1 suggests such an anomaly: is Public Storage less risky than the other top holdings?

Figure 2 shows the standard deviations of the top USMV holdings and their correlations with SPY from 11/1/2015 to 4/5/2016.

Click to enlarge

Source: Yahoo Finance

Figure 2 shows that Public Storage has a higher volatility than the other ETF components. However, it has a lower correlation with the US market than the other companies.

Figure 3 presents the correlations between the top holdings in USMV between 11/1/2015 and 4/5/2016.

Source: Yahoo Finance

Figure 3 indicates that Public Storage is relatively uncorrelated with the other top holdings. USMV will attempt to minimize volatility through exploiting these low correlations. This explains the large allocation to PSA.

Qualitative risk analysis of Public Storage

Systemic risks affecting Public Storage

According to the 2015 10K, Public Storage is the largest owner of self-storage in the U.S and accounts for 6% of square-footage. The market is fragmented and competitive. Therefore, PSA has limited ability to increase rents based upon its brand. In addition, PSA is classified as a Real Estate Investment Trust and must distribute 100% of taxable income. Therefore, it primarily relies on two factors to increase revenues, profits and distributions: 1) self-storage rents; 2) raising additional capital with advantageous terms to buy or develop new facilities. This analysis will focus on the second factor.

The need to raise capital links Public Storage with many other public companies that require external financing: Master Limited Partnerships, high-yield issuers and so forth. If such financing is expensive or unavailable, the revenues and profits of these other companies will likely decrease materially. As a result, their stock prices should fall simultaneously.

Stability of Public Storage

Figure 4 calculates the free cash flow available to common equity shareholders in 2015. Free cash flow and net income covered approximately 90% and 94%, respectively, of the dividend last year.

Source: 2015 Public Storage 10K

To be clear, Public Storage differs significantly from many other companies that persistently require outside capital. As shown in Figure 4, PSA is both profitable and generates positive free cash flow; whereas, many high yield issuers are unprofitable and bleed cash each quarter. Free cash flow nearly covers the dividend and indicates that PSA would be able to sustain its dividend through adverse funding conditions. In fact, PSA never cut its dividend during the credit crisis. Therefore, external financing primarily affects the future growth rate of its dividends, not sustaining existing distributions. By contrast, a funding drought would imperil the existence of some high yield issuers.

Valuing Public Storage

Figure 5 illustrates the implied dividend growth rates for PSA based upon a dividend discount model. This model assumes perpetual dividend growth, g, and cost of capital, r. P and D refer to the current price and dividend per share, respectively. The equation was rearranged to calculate the implied growth rate based upon the current price and dividend for various required rates of return.

Click to enlargeSource: Public Storage 2015 10K

Figure 5 shows implied dividend growth rates for PSA based upon a dividend discount model. For example, suppose you require 12% annually to compensate for the risk of holding PSA. To justify the current valuation, the dividend would need to grow approximately 9% in perpetuity. This is close to the compounded annual growth rate of the dividend since 1990.

A required return of 12% seems reasonable but the implied perpetual growth rate of 9% is less plausible. PSA would require sustained loose credit and increases in self-storage rents to justify this valuation.

Figure 6 represents the intrinsic prices per share for Public Storage based upon various dividend growth rates and required rates of return. The green prices are above the current price of $269 per share; whereas, red are beneath it.

Source: Poppertech

You can determine your own valuation based upon Figure 6.

In conclusion, Public Storage is a stable company, but its stock is likely to decline significantly if it is unable to maintain its high rate of dividend growth.

Quantitative risk analysis of Public Storage

Figure 7 depicts $100 invested in SPY and Public Storage during the credit crisis.

Click to enlarge

Source: Yahoo Finance

Figure 7 shows that PSA frequently underperformed the U.S. market during the credit crisis. As a result, PSA is riskier than current data suggest.

The volatility forecast in Figure 8 is designed to mimic a commercial risk model. Please see the note at the end of the article for details. Daily returns are blue, the upper bound of the 95% confidence interval is green, and the lower bound is red. On average, 5% of returns should fall outside of these bounds with a properly constructed risk model. In this case, 6.1% of returns lie beyond the bounds. This suggests the model fits the data reasonably well.

Source: Yahoo Finance

Figure 8 shows the historical returns of PSA since 2007 with forecasts from a risk model. The narrow bounds in the current period indicate volatility is forecast to be low relative to the past. This occurs because risk models base forecasts primarily upon the most recent history. Therefore, the volatility estimate is "blind" to the distant past and lacks any "memory" of the credit crisis.

Figure 9 illustrates 250 day rolling correlations between PSA and SPY from 2007 to present.

Click to enlargeSource: Yahoo Finance

Figure 9 shows the correlations between PSA and SPY. During the credit crisis and for a couple of years afterwards, PSA exhibited high correlations with SPY. Since 2012, correlations have lessened considerably.


If external funding becomes expensive, PSA should become more volatile and correlated with the rest of the market. It should also underperform the S&P 500. Since risk models base volatility estimates on recent history, current forecasts underestimate the risks associated with Public Storage. This problem calls into question the viability of minimum volatility as an investment strategy.

Notes: The volatility forecast uses the type of ARCH (Autoregressive Conditional Heteroskedasticity) calculations used in a commercial risk model. Forecast volatility is calculated using the past 1000 squared returns and an exponential weighting factor of .94. For example, to calculate volatility today, the squared return yesterday would have a weight of .94, the return the day before would have a weight of .94*.94, and so on. These weights were normalized to sum to one and used to calculate a weighted average of the squared returns.

Disclosure: I/we have no positions in any stocks mentioned, and no plans to initiate any positions within the next 72 hours.

I wrote this article myself, and it expresses my own opinions. I am not receiving compensation for it (other than from Seeking Alpha). I have no business relationship with any company whose stock is mentioned in this article.