Financial Education

One way to estimate VaR is to use the historical method, which graphs the actual daily returns over a user-specified past period into a histogram. For a two-year observation period (500 trading days) the 1% VaR would be the loss on the fifth-worst day, and the 5% VaR would be the loss on the 25th-worst day.

The results reflect past results, not necessarily those that will be encountered in the future. It is also important to adjust for a moving investment horizon. For example, calculating the VaR for bonds expiring in 2020 from historical results of the prior year would be best done using bonds expiring in 2019.

An advantage of the historical method is that it is non-parametric, which means it does not require assumptions for probability distribution. The disadvantage is that the past may have very different risk characteristics from the future.

Since reported hedge fund performance is of doubtful significance and risk monitoring is difficult, due diligence takes on special significance when investments in hedge funds are being considered. Some of the things investors must determine include:

1. The structure of the fund
   • Legal entity
   • Identity of manager
   • Domicile
   • Regulatory regime
2. Strategy
   • Style
   • Instruments used
   • Benchmark
   • Niche
   • Current holdings
3. Performance data since inception for all funds under management
4. Risk management
   • What risks are measured
   • How are they measured
   • How are they controlled
   • How is leverage employed
5. Research
   • Has the firm’s research led to changes in strategy
   • Strength of research efforts
   • Research budget
   • Personnel
6. Administration
   • Lawsuits
   • Employee turnover
   • Disaster recovery plans
7. Legal and Regulatory
   • Fee structure
   • Lock-up period
   • Minimum and maximum subscription amounts
   • Drawback provisions
8. References
   • Professional
   • Other investors in the fund

Over time, small capitalization stocks have been shown to outperform large-capitalization stocks. However, timing changes in the relative performance between the two groups could lead to still-better performance. In the Fall 2007 Journal of Portfolio Management, L’Her, Mouakhar and Roberge test three nonparametric techniques derived from artificial intelligence and using 20 macroeconomic and financial variables as inputs.

The three approaches are recursive partitioning, a neural network and a genetic algorithm.

Each of the three techniques outperforms a naive small-minus-big strategy, but the best results are derived from taking the consensus of the three techniques.

One of the major advantages of international diversification is to reduce overall portfolio risk because the returns on international portfolios have low correlations with the returns on domestic portfolios. However, several studies have shown that correlations across markets are higher when the U.S. market is falling than when it is rising - reducing the value of diversification just when it is needed most.

In the September 2007 Review of Financial Studies Hong, Tu and Zhou sort the CRSP database for monthly returns on 10 style portfolios and the value weighted market index. They find that the correlation asymmetry primarily exists within the four smallest size portfolios.

When considering the asymmetries from an investment decision-making perspective, the authors find that investors with disappointment aversion should reduce their exposure to risky assets, and in particular to the smallest-capitalization stocks.

With the growth in the hedge fund industry has come a decline in the value added by hedge fund managers. Given the high fees typically charged by hedge funds, some have questioned whether passive approaches can be constructed that would provide returns similar to those of hedge funds while offering greater transparency and liquidity.

In the Winter 2007 Journal of Wealth Management Harry Kat discusses three general approaches to hedge fund replication:

• Factor Models
• Mechanical Trading Rules
• The author’s FundCreator product

In a factor model, linear regressions determine the market exposures experienced by a hedge fund or hedge fund index. Factors may include stock, bond, commodity and currency returns, or changes in credit spreads and market volatility. These exposures can then be taken via index products or derivative instruments.

In the case of funds that add value by timing short-term changes in market exposure, the investor’s trading behavior can be compared to mechanical trading rules.

The FundCreator product is a risk management tool that allows the investor to target the risk and correlation properties desired in order to maximize diversification potential.

The quoted bid/ask spread is the difference between the lowest ask price for a security and the highest bid price. For small orders, the quoted spread is a good indication of the execution cost for a trade. For large orders, however, it may not fully represent the cost.

The effective spread better captures the cost of a round-trip order by including both price movement (dealers coming in to execute orders at a better price than previously quoted) and market impact (spread widening due to the size of the order itself.)

Effective spread is defined as twice the difference between the actual execution price and the market quote at the time of order entry. For example, an order is entered when the quote is $10.00/$10.20. The order is executed at $10.15. The effective spread is 2(10.15 - 10.10) = $0.10.

An unweighted securities index assigns equal value to each index component regardless of its relative price or market capitalization. It is equivalent to investing the same dollar amount in each index component.

Smaller cap stocks will receive a higher weighting in an unweighted index than they would in a value-weighted index. This can lead to a bias toward small cap stocks over time.

One way to estimate VaR is the analytical method, also called the variance-covariance method.

This method assumes a normal distribution of portfolio returns, which requires estimating the expected return and standard deviation of returns for each asset. As the number of securities in a portfolio increases, these calculations can become unwieldy. As a result, a simplifying assumption of zero expected return is sometimes made. This assumption has little effect on the outcome for short-term (daily) VaR calculations but is inappropriate for longer-term measures of VaR.

The advantage of this method is its simplicity. The disadvantage is that the assumption of a normal return distribution can be unrealistic.

There are a number of benchmarks available for hedge funds, distinguished primarily by the frequency of data reporting (monthly or daily), whether they are investable or not, and whether they list the actual funds from which they are comprised.

Principle differences among the indices include:

• Selection criteria - what kind of track record or level of assets must a fund attain in order to qualify for inclusion?
• Style classification
• Weighting scheme - usually either equal weights or based on assets under management
• How frequently the weights of the constituent funds are rebalanced
• Investability

Since hedge funds often promote themselves as absolute return vehicles (and thus do not have a direct benchmark) that absolute return nonetheless must be measured in terms of some benchmark. Important questions to consider are whether any alpha reported is sensitive to the benchmark in use and whether the alpha takes into account the true systematic risks faced by the portfolio.

There are also a number of limitations to most of the available hedge fund indices, including:

• Results are self-reported by the managers and may not be completely neutral or accurate
• Databases reflect survivorship bias as poorly performing managers exit leaving only the best included. This results in an upward bias to reported returns.
• The frequency of data reporting may lead to stale prices and distort correlation measures.
• Missing data can be filled at the manager’s convenience, leading to a backfill bias.

Studies to determine whether hedge fund returns can be mimicked using passive strategies have shown mixed results but do show that returns are influenced largely by the trading strategy employed. Market neutral strategies may offer better diversification to traditional asset classes.

Hedge fund returns have been shown to exhibit low skewness and high kurtosis, which are undesirable features. Mean-variance optimizations are sensitive to errors in the return estimates, and historical data (as discussed above) can be unreliable.

Longevity annuities exchange an up-front payment for a stream of payments that will begin some years after retirement. For example, the annuity may be purchased when the investor is 65, but only begin to pay benefits when the investor turns 80. Benefits will continue for the remainder of the investor’s life.

Investment annuity payouts per dollar invested are much higher than immediate annuity payments for several reasons:

• The lack of payouts in early years allows for greater compounding benefits on investment returns
• The shorter remaining expected life span after payouts begin allows for each payment to be larger
• Potential annuitants who die before reaching the target age subsidize returns for those who live longer

In the January/February 2008 Financial Analysts Journal, Scott argues that many investors will benefit from an allocation to longevity annuities, and that the optimal bundle depends upon the percentage of total assets the annuitant is willing to allocate to annuities. The greater the proportion annuitized, the earlier payments should start.