1 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Financial Planners recommend as investor approach retirement, portfolios should shift toward safer categories of securities, i.e., from small-cap to large-cap funds, and than few years before retirement, shifting to bonds or even Treasury bills. The problem with these recommendation is that when to shift is a guess. Explain the concept of risk aversion

2 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Life Cycle Investing and Risk Tolerance: Burton Malkeil (1996) - risk tolerance is a function of attitude toward and his/her risk capacity. Risk attitude is subjective but capacity is related to investor’s place in the life cycle. Older investors have less opportunity to recoup financial losses, thus less capacity for risk exposure. Portfolio composition will be different at different stages of their life cycle. Samuelson (1994)- younger investors may lean toward equities

3 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Because they may work harder to compensate for unlucky stock losses. McEnally (1985) - The variability of ending wealth increases as the holding period increases, i.e., risk increases as holding period lengthens. Thorley (1995) counters McEnally - greater risk is mainly uncertainty about how much better equity will do than T-bills. Only ‘upside’ uncertainty as stocks very rarely underperform bonds. Investors

4 Life Cycle Investing……. Hickman et. al, JPM Winter 01 are choosing what to invest in and not whether to Invest. Investment decisions are based on relative performance. If X is riskier than Y, but the return on X is always greater than Y, relative performance determines the correct investment choice. Probability that the higher returns will be realized increases as the holding period increases.

5 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Purpose of this Study: Quantify the likelihood that stocks will outperform bonds, and bonds will outperform bills, etc., over various holding periods. Analyze the interplay between the investment horizon and the risk-return performance over six classes of securities. Security classes are: large-cap and small-cap; intermediate and long term govt.. bonds; and corporate and Treasury bills.

6 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Useful for assessing the composition of portfolios at any point in an investor’s life cycle while allowing for individual differences for risk tolerance.

7 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Data and Methodology: Review Malkiel’s results, Exhibit 2. B has higher mean and higher standard deviation. No inference can be drawn based on the mean-variance criteria. Decision is based on individual risk tolerance. However, if B is highly correlated with A, B will always be preferred regardless of their degree of risk aversion.

8 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Data : Ibbotson and Sinquefield data over the period of (70 years) is used. Allowed two independent non-overlapping 30 year holding period to analyze. Not enough observations to draw any reliable conclusions. To remedy - sample monthly returns with replacement was used. Allowed as many holding periods of varied length to examine.

9 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Examined holding period ranging from 1 year to 30 years, drawing 500 observations per period. To construct a 10 year holding period, 120 months were randomly selected. For each month, a vector of returns for each asset type (T-bills, Intermediate Govt.. bond …...etc.) is used to form six holding- period wealth relatives, one corresponding to each security type. Wealth Relative: Return of 0.20, 0.40 and -0.05,

10 Life Cycle Investing……. Hickman et. al, JPM Winter 01 the three year wealth relative is equal to (1.2)(1.4)(0.95) = $1 invested at the beginning of the period will grow to $1.25 by the end of the period. Differences between wealth relatives are then calculated as: Small Cap - Large Cap Large Cap - Corp. Bonds Corp. Bonds - LT Govt.. Bonds LT Govt.. Bonds - Int. term Govt. Bonds Int. term Govt. Bonds - Treasury Bills

11 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Since assets and asset classes are highly correlated, relative returns (R b - R a ) are analyzed. If the distribution of pair wise return difference is positive 100% of the time, B would dominate regardless of the degree of risk aversion. Explain Exhibit 3 - Correlation matrix of assets. - Results suggest that not all assets are mutually exclusive - Explain.

12 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Exhibit 4-Descriptive statistics: Major Findings  Great difference in wealth relatives between security classes over long holding periods. 30 year holing period ending wealth: T-bill $3.03 vs. small- stock $ No advantage to investing in long-term over intermediate term govt. bonds. Explain. Risk (standard deviation) for 30 year holding period for small stocks is vs for S&P. Risk may largely offset larger return.

13 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Median yields ( for small vs for S&P) is much closer. Extreme skewness on wealth relative’s distribution. Small stock risk is mainly upside risk Exhibit 5- Percentage of Differential Wealth Relatives falling below zero. Exhibits 4 and 5- Major Findings: Benefits of moving to higher-risk classes as one’s holding periods lengthens.

14 Life Cycle Investing……. Hickman et. al, JPM Winter 01 No compelling reason to move into high risk Bonds with longer holding periods Exhibit 11contains differential mean wealth relatives data. For 20 year hp, by investing in S&P 500, one would expect to earn $8.82 over LT Corporate bonds. Median is $5.8 that indicates a positively skewed distribution. Upside uncertainly regarding the assets performance.

15 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Asset Allocation and Life Cycle Investing Malkiel Approach (in their 20s) (in their 60s) Equity 70% Equity 30% Bonds 25%Bonds 70% Cash 5% Rule of Thumb 100 minus your age, i.e, Equity 80%Equity 40% Bonds 20%Bonds 60%

16 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Implied involves discrete shifts from one asset class to another as one’s holding period shortens ad expected underperformance likelihood exceeds a critical value of 30%. S&P 500 is an indexing benchmark Equity 95% in S&P 500 T-bills 5%

17 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Exhibit 14: Mean Ending Wealth-Forty years of investing. Simulation is repeated 500 times. Modeled retirement savings by beginning with a portfolio initially valued at $100, then adding $100 to the principal each month over the 40 year period. Results in Exhibit 14 are startling. Ending wealth for S&P 500 is around $5million while traditional allocation models are around $800,000. Traditional Models avoid underperformance only

18 Life Cycle Investing……. Hickman et. al, JPM Winter 01 by 12%. Therefore, the expected cost is high in terms of foregone wealth, while the expected benefits appear insignificant. To determine whether the benefits are substantial for shorter holding period, ending portfolio values with various holding periods were computed. Exhibit 15 contains the results of 10, and 40 year investment horizons.

19 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Summary of results: Over shorter horizons, the allocation models performs better at reducing risk without causing the severe penalties for ending wealth. For a 10 year horizon, the chance that the S&P will under- perform any of the three models is 26%, almost half of 40 year horizon. Yet the implied model performs as well as S&P. For a 20 year horizon, ending wealth based

20 Life Cycle Investing……. Hickman et. al, JPM Winter 01 on Implied Model ($174,416) vs. S&P ($150,972), while S&P under-performs this portfolio by nearly 30% of the time. The traditional models severely under- performs both the Implied model and the S&P model. All models over all horizons exhibit positive skewness (mean exceeds median), i.e, potential for upside gains.

21 Life Cycle Investing……. Hickman et. al, JPM Winter 01 Conclusions: High correlations across class of securities make direct comparisons of mean and variance difficult. Relative performances are better variables to analyze. For longer holding periods, there will be significantly huge penalties for not pursuing risky investments, i.e., equities.

22 Life Cycle Investing……. Hickman et. al, JPM Winter 01 There seem to be little benefit, yet higher risk, associated with investing in longer-term bonds versus intermediate-term bonds.