The latest service on the Alpholio™ patent-based analytical platform implements the capital asset pricing model (CAPM). Specifically, the service calculates the security characteristic line (SCL) with related statistics. In addition, the service provides statistics for the difference between periodic returns of the analyzed and reference securities.

In contrast to the traditional CAPM, which uses a theoretical market portfolio as a reference, the service allows the use of any available security. This has a practical implication of comparing concrete investment vehicles as opposed to evaluating a real security against an uninvestable “market” index, such as the S&P 500®. However, in both cases the reference is a single factor, whose periodic returns try to explain the returns of the analyzed security.

To demonstrate the service in action, let’s analyze the Vanguard Health Care Fund (VGHCX, Investor Shares; VGHAX, Admiral Shares). We covered this fund in one of the previous posts. This analysis will begin in January 2013, when the fund was fully taken over by its current manager.

Here are the fund’s exposures through June 2017, derived from the Fund Analysis service:

Reference Weights for Vanguard Health Care Fund Investor Shares (VGHCX)

The fund had equivalent positions in the Guggenheim S&P 500® Equal Weight Health Care ETF (RYH), iShares Global Healthcare ETF (IXJ) and iShares U.S. Pharmaceuticals ETF (IHE). Collectively, these positions formed a reference ETF portfolio with volatility comparable to that of the fund.

Let’s use the Total Return service to determine which of these three ETFs most closely tracked the fund’s returns over the same period:

Total Return of Vanguard Health Care Fund Investor Shares (VGHCX) and Reference ETFs (RYH, IXJ and IHE)

As could be expected, RYH, the ETF with the dominant weight in the reference portfolio, turned out to be the best fit. Therefore, let’s choose this ETF as a CAPM reference for the fund, using excess (i.e. net of risk-free rate) monthly returns of both securities:

CAPM for Vanguard Health Care Fund Investor Shares (VGHCX) and Guggenheim S&P 500® Equal Weight Health Care ETF (RYH)

The beta coefficient of the fund vs. the ETF was somewhat below one, a result of the slightly lower standard deviation (see statistics below the Total Return chart) and the 0.959 correlation coefficient (separately obtained from the Correlation service). With the t-statistic much higher than two, the beta coefficient was statistically significant. The alpha intercept, while positive, was not statistically significant. With the R-squared of almost 92, the regression fit was quite good.

Here is the expanded bottom panel of statistics:

Return Difference Statistics for Vanguard Health Care Fund Investor Shares (VGHCX) and Guggenheim S&P 500® Equal Weight Health Care ETF (RYH)

The mean difference between monthly returns of the fund and the ETF was slightly negative and had a substantial standard deviation. The low t-statistic indicated that the return difference was not statistically significant. By this measure, any value subtracted by active management of the fund could be attributed to bad luck and not a lack skill. If performance of the fund and the ETF were unchanged, it would take almost 212 years for the return difference to become statistically significant (and still be negative).

Since the fund had a considerable portion of its assets in foreign equities, IXJ could also be a relevant CAPM reference:

CAPM for Vanguard Health Care Fund Investor Shares (VGHCX) and iShares Global Healthcare ETF (IXJ)

In this case, the alpha intercept was large and statistically significant, although the R-squared was slightly lower. Similarly, the average return difference was a positive 0.35% and was statistically significant, requiring only 3.1 years to become so (statistics not shown here for brevity). This underscores that the choice of an appropriate reference security is critical because the CAPM regression uses only a single explanatory variable.

To try the new CAPM service, please register on our website.

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