**Revisiting value of active management over index funds**

*By Stanislaw Zarzycki and Kenneth C Marshall*

It has been a while since the economics guru Burton Malkiel published his seminal study "A Random Walk Down Wall Street" in 1973. Professor Malkiel became the leading proponent of the idea that active managers cannot outperform their index in the long run ** ^{1}**. Over the past 40 years, the efficient market hypothesis has served to give birth to the whole index/ETF craze and to question the value-add of active fund managers.

Also over the past 40 years, managers got smarter, information flow became more efficient and data more accessible. We've seen the rise of the internet and instant messaging and vastly more powerful analytic tools. Surely active managers have gotten better at the game and better at spotting inefficiencies.

But wait: does this mean instead that markets are now more efficient because all information, including private information, are incorporated in price? Are active managers, despite having more resources, becoming less effective and relevant?

In this age of instant information, we thought it highly relevant to retest the general hypothesis: do active managers outperform the market (maintaining their relevance) or does the "more-efficient" market hypothesis still prevail? To test this question, we used the Morning Star mutual fund database to focus on US large cap blend managers over the period 1999-2012. This period encompasses 3 economic cycles and the rise of the age of instant information.

The initial task was to refine the database down to large cap managers focused on US equities (> 95% of portfolio invested in US equities, > 90% invested in large cap stocks). This was not a straightforward exercise as managers evidently drifted to foreign stocks or mid cap companies in search of performance. Our filter ( US and large cap) narrowed the list of mutual fund managers down from 27,736 to 158 funds whose performance went back to at least 1999.

We then compared the compounded return of these 158 mutual funds managers to the S&P500 total return index. Remarkably, 47 or 29.75% of these managers outperformed the index. One could conclude that, yes, about 1/3 of the active managers appear to defy the efficient market hypothesis. But this is not determinative of anything (contrary to some Wall Street analysts). One needs to take the analysis one step further and ask if there is any predictive power in these past outperformer returns as to future outperformance? That is to say, how many of these 47 *consistently* outperformed the market?

We chose to slice the data into two periods: 1999-2005 and 2006-2012. We used the compounded return over the earlier period (1999-2005) to select managers that initially outperformed the index to find out if their prior record had much bearing on the future relative performance. Out of the 54 funds (34%) that outperformed over the in-sample 7 year period (1999-2005), only 7 (13%) outperformed the S%P 500 over the following 7 year period 2006-2012. If we then eliminate duplicate funds (funds managed by the same manager) in our sample, only __3.7%__ of the mutual funds continued outperforming the index in the out-of-sample period (2006-2012). This would indicate that 96.3% of actively managed funds *underperformed* the S&P.

The initial conclusion based on our subset of managers is that a reasonable percent of them *can* outperform the index over the long run. However, choosing those managers based on past performance (so-called "tail chasing"), is a losing proposition: the odds are overwhelmingly against you. In other words, there is significant mean reversion of returns among active managers consistent with Malkiel's random walk proposition. As for those few managers who beat the odds and consistently outperformed the index, one has to question how they did it. Did they aggressively use cash as an asset class/hedging strategy? The answer may reveal an imperfection in the efficient market hypothesis and provide a clue on picking those active managers who truly provide value-add. For the other 96% of managers, one's investment dollar is better spent on a random walk with ETF's.

1. We recognize that the term "efficient market" is attributable to Eugen Fama "Random Walks In Stock Market Prices", *Financial Analysts Journal* in 1965.

**Disclosure: **I am long [[SPY]].

**Revisiting value of active management over index funds**

*By Stanislaw Zarzycki and Kenneth C Marshall*

It has been a while since the economics guru Burton Malkiel published his seminal study "A Random Walk Down Wall Street" in 1973. Professor Malkiel became the leading proponent of the idea that active managers cannot outperform their index in the long run ** ^{1}**. Over the past 40 years, the efficient market hypothesis has served to give birth to the whole index/ETF craze and to question the value-add of active fund managers.

Also over the past 40 years, managers got smarter, information flow became more efficient and data more accessible. We've seen the rise of the internet and instant messaging and vastly more powerful analytic tools. Surely active managers have gotten better at the game and better at spotting inefficiencies.

But wait: does this mean instead that markets are now more efficient because all information, including private information, are incorporated in price? Are active managers, despite having more resources, becoming less effective and relevant?

In this age of instant information, we thought it highly relevant to retest the general hypothesis: do active managers outperform the market (maintaining their relevance) or does the "more-efficient" market hypothesis still prevail? To test this question, we used the Morning Star mutual fund database to focus on US large cap blend managers over the period 1999-2012. This period encompasses 3 economic cycles and the rise of the age of instant information.

The initial task was to refine the database down to large cap managers focused on US equities (> 95% of portfolio invested in US equities, > 90% invested in large cap stocks). This was not a straightforward exercise as managers evidently drifted to foreign stocks or mid cap companies in search of performance. Our filter ( US and large cap) narrowed the list of mutual fund managers down from 27,736 to 158 funds whose performance went back to at least 1999.

We then compared the compounded return of these 158 mutual funds managers to the S&P500 total return index. Remarkably, 47 or 29.75% of these managers outperformed the index. One could conclude that, yes, about 1/3 of the active managers appear to defy the efficient market hypothesis. But this is not determinative of anything (contrary to some Wall Street analysts). One needs to take the analysis one step further and ask if there is any predictive power in these past outperformer returns as to future outperformance? That is to say, how many of these 47 *consistently* outperformed the market?

We chose to slice the data into two periods: 1999-2005 and 2006-2012. We used the compounded return over the earlier period (1999-2005) to select managers that initially outperformed the index to find out if their prior record had much bearing on the future relative performance. Out of the 54 funds (34%) that outperformed over the in-sample 7 year period (1999-2005), only 7 (13%) outperformed the S%P 500 over the following 7 year period 2006-2012. If we then eliminate duplicate funds (funds managed by the same manager) in our sample, only __3.7%__ of the mutual funds continued outperforming the index in the out-of-sample period (2006-2012). This would indicate that 96.3% of actively managed funds *underperformed* the S&P.

The initial conclusion based on our subset of managers is that a reasonable percent of them *can* outperform the index over the long run. However, choosing those managers based on past performance (so-called "tail chasing"), is a losing proposition: the odds are overwhelmingly against you. In other words, there is significant mean reversion of returns among active managers consistent with Malkiel's random walk proposition. As for those few managers who beat the odds and consistently outperformed the index, one has to question how they did it. Did they aggressively use cash as an asset class/hedging strategy? The answer may reveal an imperfection in the efficient market hypothesis and provide a clue on picking those active managers who truly provide value-add. For the other 96% of managers, one's investment dollar is better spent on a random walk with ETF's.

1. We recognize that the term "efficient market" is attributable to Eugen Fama "Random Walks In Stock Market Prices", *Financial Analysts Journal* in 1965.

**Disclosure: **I am long [[SPY]].

**Mean-Variance Optimization vs. Naive Diversification in Portfolio Allocation**

In response to the blog post "Understanding the Perils of Mean-Variance Optimization" written by Newfound Research on Seeking Alpha (posted Feb 26th, 2013), we wanted to test firsthand the utility of the MVO technique applied to asset allocation. We can start with a simplified unconstrained MVO model.

We take a base case scenario of a "naive" diversification (50:50) by investing equal dollar amounts between two assets - the S&P 500 futures (ticker: SP) and 30 Year Treasury bond futures (ticker: US) contracts - and back-test over a long period (1990-2012). The allocation was rebalanced on a weekly basis in order to keep us as tightly constrained as possible to the 50:50 allocation.

Having developed a base case portfolio (naive 50:50 allocation model), we can then build out an unconstrained MVO model. The unconstrained, or actively re-balanced, portfolio also invests in the same two assets (SP and US futures contracts), but with allocation weights determined by the change in ratios of the average return to variance or volatility. If for example:

SP: (Avg daily return = 0.04%; Variance = 0.02%)

US: (Avg daily return = 0.03%; Variance = 0.01%)

Then the conversion factor for US = 0.02% / 0.01% = 2

Using the conversion factor of 2, we come up with the weights:

W(SP) = 0.04 / (0.04 + 0.03 * 2) = 0.4

And

W(US) = (0.03 * 2) / (0.04 + 0.03 * 2) = 0.6

We then run a back-test on these two simple re-balancing techniques (50:50 and MVO) in order to compare the two methods. The results can be seen below:

The results show an improved historical performance in the case of the MVO technique but the question remains: are they statistically significant (at 5% significance level)? To answer that question we performed a bootstrap test:

1. Take the equity curve of MVO model and subtracted the equity curve of 50:50 model to extract the excess returns attributable to the MVO process.

2. Normalize the new equity curve (excess returns) by subtracting the average return of the series from each daily return - zero centering

3. For each resample, select n instances of adjusted returns, at random (with replacement), and calculate their mean daily return (bootstrapped mean).

4. Perform 1000 of re-samples to generate a large number of bootstrapped means.

5. Form the sampling distribution of the means generated in the step above.

6. Derive the p-value of the initial back-test mean return (non zero-centered) based on the sampling distribution

The bootstrap results showed that the Z score was 0.478 which translates into a *p* value of 0.316 which falls __short__ of being statistically significant at a 5% level.

In conclusion, the above exercise showed that using a MVO technique to asset allocation versus a naive 50:50 diversification did __not__ add value at least for the use of those two instruments.

We will follow up with the results of the next logical step: how does a *constrained* MVO.

**Disclosure: **I am long [[TLT]], [[SPY]].

**Additional disclosure:** I actively trade a systematic macro strategy. My current positions include the following equities: SPY, TLT.

**Mean-Variance Optimization vs. Naive Diversification in Portfolio Allocation**

In response to the blog post "Understanding the Perils of Mean-Variance Optimization" written by Newfound Research on Seeking Alpha (posted Feb 26th, 2013), we wanted to test firsthand the utility of the MVO technique applied to asset allocation. We can start with a simplified unconstrained MVO model.

We take a base case scenario of a "naive" diversification (50:50) by investing equal dollar amounts between two assets - the S&P 500 futures (ticker: SP) and 30 Year Treasury bond futures (ticker: US) contracts - and back-test over a long period (1990-2012). The allocation was rebalanced on a weekly basis in order to keep us as tightly constrained as possible to the 50:50 allocation.

Having developed a base case portfolio (naive 50:50 allocation model), we can then build out an unconstrained MVO model. The unconstrained, or actively re-balanced, portfolio also invests in the same two assets (SP and US futures contracts), but with allocation weights determined by the change in ratios of the average return to variance or volatility. If for example:

SP: (Avg daily return = 0.04%; Variance = 0.02%)

US: (Avg daily return = 0.03%; Variance = 0.01%)

Then the conversion factor for US = 0.02% / 0.01% = 2

Using the conversion factor of 2, we come up with the weights:

W(SP) = 0.04 / (0.04 + 0.03 * 2) = 0.4

And

W(US) = (0.03 * 2) / (0.04 + 0.03 * 2) = 0.6

We then run a back-test on these two simple re-balancing techniques (50:50 and MVO) in order to compare the two methods. The results can be seen below:

The results show an improved historical performance in the case of the MVO technique but the question remains: are they statistically significant (at 5% significance level)? To answer that question we performed a bootstrap test:

1. Take the equity curve of MVO model and subtracted the equity curve of 50:50 model to extract the excess returns attributable to the MVO process.

2. Normalize the new equity curve (excess returns) by subtracting the average return of the series from each daily return - zero centering

3. For each resample, select n instances of adjusted returns, at random (with replacement), and calculate their mean daily return (bootstrapped mean).

4. Perform 1000 of re-samples to generate a large number of bootstrapped means.

5. Form the sampling distribution of the means generated in the step above.

6. Derive the p-value of the initial back-test mean return (non zero-centered) based on the sampling distribution

The bootstrap results showed that the Z score was 0.478 which translates into a *p* value of 0.316 which falls __short__ of being statistically significant at a 5% level.

In conclusion, the above exercise showed that using a MVO technique to asset allocation versus a naive 50:50 diversification did __not__ add value at least for the use of those two instruments.

We will follow up with the results of the next logical step: how does a *constrained* MVO.

**Disclosure: **I am long [[TLT]], [[SPY]].

**Additional disclosure:** I actively trade a systematic macro strategy. My current positions include the following equities: SPY, TLT.