Hakan Saraoglu

How Many Mutual Funds Are Needed to Form a Well- Diversified Asset Allocated Portfolio?

Funds of funds, which have become a popular investment vehicle in recent years, diversify across asset classes as well as managers with different styles and expertise. Lifecycle funds are a good example of funds of funds where investors can invest in a group of asset classes in different proportions depending on their investment horizon, risk tolerance, and objectives. Given that the number of mutual funds in the portfolios of lifecycle funds offered by different investment companies varies significantly even for those with similar targets, it is important to investigate the relationship between the number of mutual funds in an asset allocated portfolio and the resulting diversification benefits. As investors in lifecycle funds are concerned with the level of wealth they will have accumulated as of a target date, the variability of terminal wealth at the end of a given holding period is a relevant measure of risk for their portfolios. In this article the authors use a survivorship-bias-free sample to assess the impact of the number of mutual funds in an asset allocated portfolio on the variability and shortfall risk of its terminal wealth. Specifically, they run simulations to generate a large number of terminal wealth level outcomes for a portfolio with a given number of funds. Then, they obtain the frequency distribution of the terminal wealth outcomes, and use its dispersion as the risk measure in the analysis. The findings for three asset allocation scenarios, which are reported for 5-year and 10-year investment horizons, indicate that holding 10 to 12 funds in the portfolio instead of the minimum possible 2 funds as dictated by the asset allocation to equity and bonds reduces the standard deviation of terminal wealth by about 60%. This reduction can be obtained without sacrificing expected terminal wealth levels, and hence without a reduction in total returns. Similarly, the mean shortfall of terminal wealth and the semivariance of terminal wealth are reduced by 60% and 85%, respectively.

Performance Implications of Holding Multiple Mutual Funds with the Same Investment Objective

In this study we investigate the potential benefits of holding multiple mutual funds with the same fund objective. Given that a typical investors asset allocation may involve multiple asset classes, we report results for an array of mutual fund types including aggressive growth, international equity, high quality bond, balanced, and tax-free money market funds. We measure the impact of holding multiple funds with the same investment objective on the standard deviation, mean shortfall, and semivariance of terminal wealth. Our results, which are reported for 5-year, 7-year, and 10-year holding periods, indicate that, with the exception of money market funds, it takes 5 to 6 mutual funds to reduce the variability of terminal wealth significantly regardless of fund objective. The finding for aggressive growth mutual funds is robust to controls for style differences. In other words, it still takes 5 to 6 mutual funds to diversify manager risk when we classify aggressive growth funds into small, large, value, and growth style groups. We find that the standard deviation of terminal wealth and the shortfall risk of holding a tax-free money market fund are very small in relation to the expected terminal wealth level. Thus, diversification is not a particularly relevant concern for this asset class. We also investigate how the performance of a portfolio of multiple funds in a given asset class compares with that of the benchmark portfolio for the asset class. We show that during our sample period of 1993-2002 on average aggressive growth and high quality bond funds underperform their benchmark market indices, and that holding multiple mutual funds with the same objective does not mitigate this underperformance problem. An important contribution of our study is its use of a sample that is free of survivorship bias.

Competition and Innovation in Option-Market Models

The equity options market has shown rapid growth and the competition among different options exchanges and trading platforms has intensified in recent years. As growth and competition in the U.S. options market continues, it becomes increasingly important for market participants to evaluate market quality in different options trading venues. A sound comparison of market quality among the competing trading markets requires a clear understanding of their specific market structures, since each venue attempts to differentiate itself with a unique value proposition. This article provides a review of the market microstructures of the major options exchanges and trading platforms in the United States. Using a sample period around the entry of the NASDAQ Options Market and the BATS Options Exchange, it analyzes the competition for trading volume in the options industry, investigates the characteristics of trades and execution costs in the major options exchanges and trading platforms, and examines the determinants of execution location for trades. It shows that during the first three months of their operations, the NASDAQ Options Market and BATS Options Exchange do not make a big impact on the trading volumes of the other options exchanges. It also finds that the NASDAQ Options Market has the smallest quoted spread and effective spread values for equity options among the seven exchanges during the first three months of its market entry. The BATS Options Exchange shows lower average trade size and average dollar trade size, and does not demonstrate competitive execution quality indicators or competitive execution costs in the earlier months of its operation. A probit analysis confirms that in spite of the increasingly complex and nuanced nature of options exchange competition, the main factors determining execution location for new market entrants are: i) posting quotes at the NBBO; and ii) being alone at the NBBO.