FNCE 3030 - Week 8: Asset Allocation Methods and Measures of Investment Return

Risk-Adjusted Return: Sharpe Ratio

* describes the average excess return-to-risk trade-off and is typically used to assess alternative investment opportunities (rp - r f )/ σp rp = average return of portfolio during the period rf = average risk-free rate during the period σp = standard deviation of portfolio during the period Note - since the ratio compares excess return to standard deviation it look at total risk *Appropriate for individual securities since it describes return to security's risk * Appropriate for portfolio that has a coefficient of determination (correlation coefficient 2) ≤.70, as compared to the market (e.g., small- and mid-cap stocks, alternatives, etc.)

Asset Allocation Methods

1) Modern Portfolio Theory (statistical mean-variance optimization) 2) Life cycle investment strategy 3) Practical Approaches * adjust for 60/40 mix * "Bucket" approach

Calculate Simple Interest after one year * Annual Rate = 8% * Quarterly Compounding * Initial Investment = 10,000

10,800

Calculate compounding interest after one year * Annual Rate = 8% * Quarterly Compounding * Initial Investment = 10,000

10,824.32

What is the effective annual rate given that the annual rate of return is 10% and there are 12 compounding payments per year?

10.47%

Application of Life Cycle Strategy

100 - Age Individual, age 20 * 80% invested in equities and alternatives * 20% invested in bonds and cash equivalents Individual, age 40 * 60% invested in equities and alternatives * 40% invested in bonds and cash equivalents Individual, age 60 * 40% invested in equities and alternatives * 60% invested in bonds and cash equivalents

Annualized Holding Period

Annualized HPR, given quarterly returns= [(1 + HPR1) x (1 + HPR2) x (1 + HRP3) x (1 + HPR n)] -1 Annualized HPR, given 3-year HPR= (1 + HPR1)(1/N) -1

Asset Categories

Asset allocation involves creating an appropriate portfolio mix that incorporates various asset categories: * Equities (stocks) * Fixed Income (bonds) * Real Estate * Cash Equivalents (short-term securities) * Alternative Classes

Time Weighted Return: Geometric Returns

Average compounded growth rate of the investment portfolio, calculated by using the product of the returns * Useful in explaining how much a portfolio would have grown over a time period

Other Approaches: Risk-Return Bucket Approach

Categorize investor based on individual factors * Conservative investor (50/50, 40/60, 30/70) * Moderate investor (60/40) * Assertive investor (70/30) * Aggressive investor (80/20)

Risk-Adjusted Return: Treynor Ratio

Describes the average excess return-to-risk trade-off and is typically used to assess alternative portfolios because beta replaces standard deviation (rp - r f )/ βp rp = average return of portfolio during the period rf = average risk-free rate during the period βp = portfolio's beta Note - since the ratio compares excess return to beta it look at systematic risk * Appropriate for a well-diversified portfolio that has a coefficient of determination (correlation coefficient 2)≥.70, as compared to the market * Appropriate for a well-diversified, large-cap portfolio

Given: 8% annual return, with four compounding payment periods in the year Given: 8% annual return, with daily compounding payment periods in the year

EAR = (1 + .08/4) 4 - 1 = 1.024 - 1 = 8.2432% EAR = (1 + .08/365) 365 - 1 = 1.000021918365 - 1 = 8.3278%

Calculate compounding interest at end of quarter and end of year * Annual Rate = 8% * Quarterly Compounding * Initial Investment = 10,000

End of quarter = 10,201.01 End of year = 10,832.87

Risk-Adjusted Return: Information or Appraisal Ratio

IR = (r(active mgr) - r(benchmark))/ std dev (r(active)-r(benchmark)) * The ratio appraises the portfolio manager's performance by comparing the portfolio return to the bench market return, adjusted for tracking error. * The tracking error compares the standard deviation of manager's active portfolio return to the benchmark return

Risk-adjusted return: Jenson

Jensen Index = αp = rp - [ r f + βp ( rm - r f)] * The portfolio's excess return (alpha) over the expected market return as predicted by the capital asset pricing model • The Jensen Index measures the volatility of the diversified portfolio relative to an index or market. • A positive alpha indicates good performance; a negative alpha indicates sub-performance.

Portfolio Optimization

Linear constraint for required rate of return or maximum level of risk (standard deviation)

Portfolio Rebalancing

Maintaining your asset allocation * Application of buying high and buying low Rebalancing Rules * Fixed-percentage threshold rule * Percent variance from threshold * Calendar (semi-annually, annual) * After a major market event

Assessing Risk Tolerance

Risk tolerance cannot be measured with complete accuracy * Attitude: responses to the risk tolerance questionnaire * Financial Capacity: includes assets, cash flows and life-cycle considerations * Knowledge: investments knowledge * Propensity: past investing activity

Simple Versus Compound Return

Simple Interest: Interest applied to only the beginning contribution • Example $10,000 earns 5% interest for 10 years = 500 x 10 = total $15,000 Compound Interest: Interest applied to beginning contribution plus annual additions • Example: N = 10, I = 5%, PV = 10,000, PMT = 0, FV = ? = $16,388.95

Other Approaches: 60/40 Adjustment

Start from 60% growth vs 40% income mix * Adjusts to 70/30 or 80/20, if individual factors warrant * Adjusts to 50/50 or 40/60, if individual factors warrant

Sub-Asset Categories

Stocks (equities) * Large companies (>$10 billion) • Mid-cap ($2-10 billion) • Small-cap (below $2 billion) • Domestic or foreign shares • Growth versus value stocks Bonds (fixed income) • U.S. Government Notes and Bonds • Municipal debt (state and local) • Corporate coupon bonds - investment grade, - below investment grade - "junk" bonds • Corporate zero-coupon bonds • Mortgage-backed bonds • Treasury Inflation Protected Securities (TIPS) • Foreign bonds

Strategic versus tactical allocation

Strategic allocation: * establishing a long-term target strategic allocation * portfolio monitoring and periodic rebalancing to maintain target mix Tactical Allocation: * Overweighting of asset categories based on projected performance * minimum and maximum allocations might be established

Asset Allocation Adjustments for Individual Factors

Variables influencing the asset allocation decision: * Tolerance for risk (portfolio volatility) * Financial need and return objective *Time horizon * Financial capacity * Investment knowledge * Investing experience * Preference and constraints

Life Cycle Investment Strategy

Wealth = financial wealth + human capital wealth Personal wealth is a function of financial wealth and present value of human capital * Greater the human capital (i.e. earnings capacity) the greater focus on growth investments * Lower the human capital the greater the focus on income-producing investments

Time Weighted Return

is not affected by the timing of the portfolio cash flows. It simply measures portfolio return during period .• Holding period return (total return) • Arithmetic and geometric average returns

Effective Annual Rate

is the annual rate that produces ending value(1 + period rate of interest) n where "n" = # of compounding periods

Time Weighted Return: Arithmetic Returns

um the series of returns and divide by the number of returns * Used to calculate the variance of an individual asset *Best used when forecasting a future return * Used for portfolio optimization data inputs