Analysis of Fidelity Contrafund
analysis, mutual fund

Fidelity Contrafund (ticker symbol FCNTX) is a mutual fund with approx. $61.5 billion in net assets managed by William Danoff. Currently, Morningstar rates the fund Four Stars / Silver in the US OE Large Growth category. The latest Morningstar report on the fund, titled “Still a category leader” was published in January 2013. At present, this no-load fund has a total expense ratio of 0.74%. Let’s analyze the fund’s performance using the Alpholio™ methodology.

First, the total return chart, which assumes reinvestment of all distributions into the fund and each member of the reference portfolio, respectively:

Cumulative Return of FCNTX and Reference Portfolio

The chart shows that from early 2005 to early 2009, performance of the fund was generally matched by that of its reference portfolio. From then on, the fund significantly underperformed.

This is further illustrated by the cumulative RealAlpha™ chart:

Cumulative RealAlpha™ for FCNTX

In the chart, the lag cumulative RealAlpha™ curve overlaps, for the most part, the regular RealAlpha™ curve from 2005 through 2008. Typically, this is an indication that the fund manager did not make any major directional bets that significantly departed from the fund’s holdings in the immediately preceding time window. From 2009 onwards, this approach changed; however, the net result was an undesirable downward trend of the cumulative RealAlpha™.

The overall statistics further underscore the unimpressive performance of the fund, esp. in the second part of the analysis period:

FCNTX Statistics

At about 15%, the fund’s volatility, measured by an annualized standard deviation of monthly returns in the entire analysis period, was slightly lower than that of the overall stock market. The volatility of the reference portfolio was just slightly higher than that of the fund. This typically indicates that the fund was well diversified and contained positions generally present in the reference exchange-traded products (ETPs). The discounted annualized RealAlpha™ of the fund was approx. negative 1%, which was mostly caused by a significant loss of alpha since 2009. At 0.89, the fund’s RealBeta™ was lower than that of the market, which was also reflected in the lower volatility.

The following chart demonstrates the use of smoothed RealAlpha™ to automatically generate a hypothetical trading signal for the fund:

Buy-Sell Signal for FCNTX (Smooth)

The analysis starts with an assumption that the investor initially bought the fund in early 2005 and intended to hold this investment indefinitely, i.e. at least through early 2013. The blue curve depicts the cumulative RealAlpha™ in that entire period. Since there is some degree of high-frequency oscillation in that curve, its longer-term trend can be elicited from its smoothed approximation, depicted by the green curve. Subsequently, a simple decision criterion is applied to determine whether the investment in the fund should be retained. As long as the fund generates positive monthly increments to cumulative RealAlpha™, the investment in the fund is considered beneficial. Conversely, if the fund’s cumulative RealAlpha™ begins to consistently decrease, the investment is no longer considered attractive.

The signal would allow an investor to avoid the long period of the fund’s underperformance that began in late 2008 according to the smoothed RealAlpha™ measure.

The following chart shows the major investment “themes” of the fund over time:

Reference Weights for FCNTX

In the analysis period, the fund held equivalent equity positions in JKE (iShares Morningstar Large-Cap Growth ETF; average weight of 21.8%), QQQ (PowerShares QQQ™ ETF; 17.5%), JKH (iShares Morningstar Mid-Cap Growth ETF; 14.4%), PWC (PowerShares Dynamic Market Portfolio ETF; 9.2%), EEM (iShares MSCI Emerging Markets ETF; 7.2%), and VDC (Vanguard Consumer Staples ETF; 6.7%).

The fund’s equivalent cash position in SHY (iShares 1-3 Year Treasury Bond ETF) was at times as high as 17.8%. This indicates major market timing efforts in the fund an investor would reasonably expect to be predominantly invested in equities.

For clarity, smaller reference positions are collectively represented by the Other category in the chart. For example, this category includes an equivalent position in IXJ (iShares Global Healthcare ETF; average weight of 4.6%). This position implies that the fund held equities with a significant exposure to the domestic and foreign healthcare sector.

While the Morningstar analyst report says that

“Despite its size, Fidelity Contrafund remains ahead of the game.”

this analysis clearly demonstrates that the strategy of the fund could easily be replicated using a relatively small number of exchange-traded products (ETPs), and with a better performance (higher return with comparable volatility). Investors could instead use the results of the ongoing Alpholio™ analysis to construct a substitute portfolio of liquid, low-cost instruments that provide an even higher diversification (as of the latest filing, the fund held about 375 securities).


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ETP Tracking Errors on the Rise
exchange-traded product

A recent article from InvestmentNews indicates that the tracking errors of exchanged-traded products (ETPs) are on the rise. (Tracking error is a measure of how well an ETP matches its underlying index.) An Alpholio user might therefore be concerned with the effects of this trend on the results of our analyses of mutual funds and investment portfolios. There is actually no impact: In all its analyses, Alpholio always uses real (market) returns of both the analyzed and reference instruments instead of artificial (and hence practically unrealizable) indices. Therefore, in this context the tracking error is immaterial, as is the actual index the ETP decides to track.

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How Much to Invest with Active Managers
active management, mutual fund

A recent article from Investment News discusses a simple approach to choosing actively-managed mutual funds: Focus on those funds that simultaneously have low expense ratios and managers who “eat their own cooking.” The article states

“The real eye-opener, however, is when you look at funds with both low expense ratios and managers who invest at least $500,000 in their own funds.

That leaves only 55 funds, most of which have household names like American Funds, Fidelity, T. Rowe Price, and Vanguard. But more than half of this group, 55%, has beaten the S&P 500 over the five years ending March 26.

If you stretch the time horizon to 10 years, the group does even better. Nearly seven out of 10 of these funds beat the S&P 500 over that time period.”

So, assuming that in the next 10 years the odds of picking a market-beating fund hold at approx. 70%, what percentage of assets should an investor devote to such funds? The answer can be derived from the Kelly criterion:

f = 2p – 1

where f = fraction of assets to invest with managers screened in the above manner, and p = probability of selecting an index-winning manager. The formula is intuitive: Suppose p = 50%, which means an investor has an even chance of selecting or not selecting the index-beating managers. Then f = 0%, i.e. the investor should not bet at all. On the other hand, if p = 100%, then the investor is assured to pick index-winning managers, so he/she should invest f = 100% with them.

With p = 70%, f = 40%, with the assumption that the investor periodically reassesses the situation and reallocates his/her investments (i.e. it is like a series of bets on active managers). This implies, though, that the rest, or 60%, of the investable assets should go into passive index instruments. However, if the timeframe is five years and p = 55%, then the bet on active management should only be 10%.

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Analysis of Matthew 25 Fund
analysis, mutual fund

Matthew 25 (ticker symbol MXXVX) is a mutual fund with approx. $489 million in assets managed by Mark Mulholland. Currently, Morningstar rates the fund Five Stars in the US OE Large Growth category. The last Morningstar report on the fund was published back in 2007. Currently, this no-load fund requires a minimum $10,000 investment. Let’s appraise the fund’s performance using the Alpholio™ methodology.

First, the total return chart, which assumes reinvestment of all distributions into the fund and each member of the reference portfolio, respectively:

Cumulative Return of MXXVX and Reference Portfolio

The chart shows that the fund underperformed its reference portfolio from early 2005 to late 2011. Subsequently, the total return of the fund exceeded that of both the regular and lag reference portfolios.

This is further illustrated by the cumulative RealAlpha™ chart:

Cumulative RealAlpha™ for MXXVX

In the chart, the lag cumulative RealAlpha™ curve overlaps, for the most part, the regular RealAlpha™ curve from 2005 through 2008. Typically, this is an indication that in that period the fund manager did not make any major directional bets that significantly departed from the fund’s holdings in the immediately preceding time window. From 2009 onwards, the manager changed that strategy and started to generate positive increments to RealAlpha™. However, at the end of 2011 the fund’s cumulative RealAlpha™ was barely restored to the level at which it was back at the beginning of 2005; the loss of alpha in 2006-07 was very significant.

The overall statistics further underscore the uneven performance of the fund:

MXXVX Statistics

At over 21%, the fund’s volatility, measured by an annualized standard deviation of monthly returns in the entire analysis period, was significantly higher than that of the overall stock market. The volatility of the reference portfolio was lower than that of the fund by about 3%. This typically indicates that the fund was not well diversified and carried a substantial amount of idiosyncratic risk. The annualized discounted RealAlpha™ of the fund was approximately zero, which was mostly caused by a large loss (about 25%) of alpha in 2006-07. The lag RealAlpha™ was slightly positive, mostly thanks to the fund’s outperformance in 2010-12. The RealBeta™ was significantly higher than a reference value of one.

The following chart demonstrates the use of smoothed RealAlpha™ to automatically generate a hypothetical trading signal for the fund:

Buy-Sell Signal for MXXVX (EMA)

The analysis starts with an assumption that the investor initially bought the fund in early 2005 and intended to hold this investment indefinitely, i.e. at least through early 2013. The blue curve depicts the cumulative RealAlpha™ in that entire period. Since there is some degree of high-frequency oscillation in that curve, its longer-term trend can be elicited from a smoothed approximation by an exponential moving average (EMA), depicted by the green curve. Subsequently, a simple decision criterion is applied to determine whether the investment in the fund should be retained. As long as the fund generates positive monthly increments to cumulative RealAlpha™, the investment in the fund is considered beneficial. Conversely, if the fund’s cumulative RealAlpha™ begins to consistently decrease, the investment is no longer considered attractive.

The signal would allow an investor to avoid long periods of the fund’s underperformance, while capturing most of the generation of positive RealAlpha™ (the signal does not take into account the 2% redemption fee for shares held for one year or less). Time will tell if the most recent decline in cumulative RealAlpha™ turns into a sell signal based on the EMA.

The following chart shows the major investment “themes” of the fund over time:

Reference Weights for MXXVX

In the analysis period, the fund held equivalent equity positions in JKL (iShares Morningstar Small-Cap Value ETF; average weight of 28.2%), VFH (Vanguard Financials ETF; 19.2%), VCR (Vanguard Consumer Discretionary ETF; 19.1%), MTK (SPDR® Morgan Stanley Technology ETF; 6.1%), and VOX (Vanguard Telecommunication Services ETF; 6.1%).

The fund’s equivalent cash position in LQD (iShares Investment Grade Corporate Bond ETF) was at times as high as 24.3%. This indicates major market timing efforts in the fund an investor would reasonably expect to be predominantly invested in equities.

For clarity, smaller reference positions are collectively represented by the Other category in the chart. For example, this category includes an equivalent position in EWH (iShares MSCI Hong Kong ETF; average weight of 4.2%). This position implies that the fund held equities with a significant exposure to the China market.

A recent article from Bloomberg says that:

“The fund returned 13.1 percent annualized during the five years ended on Feb. 15 compared with 4.7 percent for the S&P 500 (SPX). Matthew 25 (MXXVX) gained 26.8 percent over three years and 25.4 percent in one year. Those results make Mulholland’s fund No. 1 in the U.S. diversified stock category in Bloomberg Markets magazine’s annual ranking of mutual funds.”

Unfortunately, it seems that the focus of Bloomberg’s rankings is primarily on absolute returns, and only secondarily on risk adjustment – the Sharpe ratio over three- and five-year periods. Given its concentrated portfolio (23 stocks in the last disclosure), measuring the fund’s performance with a single factor (“the market” in CAPM) is inadequate. In contrast, the Alpholio™ methodology continuously finds a proper benchmark for the ever-changing holdings of the analyzed fund, esp. a non-diversified one.

In addition, Bloomberg’s statistics do not go back in time beyond the latest five-year period. With the underperformance of the fund in 2006-07 clearly demonstrated in this analysis, and the fact that the fund has been continuously managed by the same manager since 1996, this limited period of assessment is inadequate as well.


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Sharpe Ratios of Low-Volatility ETFs
analysis, exchange-traded fund

A recent article on Barron’s compared the returns of two low-volatility ETFs, SPLV and USMV, to that of the S&P 500® index. However, returns (even if total, not just price returns) do not tell the whole story. After all, the main feature of these two ETFs is low volatility.

One of alternative ways of assessing relative performance is the Sharpe Ratio. Since the two ETFs in question have less than three years of history, popular online services do not yet provide this measure. So, we did the calculations based on the common historical period from November 1, 2011 to March 1, 2013 for both funds, and used SPY as an implementation of the S&P 500® index. The results are:

ETF SPY SPLV USMV
Sharpe Ratio 2.13 2.82 2.93

Although SPY beat both ETFs in terms of the total return, each of them had a higher Sharpe Ratio. While the analysis period was relatively short (16 months), this bodes well for the future.

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