SAPM Capital Allocation Line Slope of the CAL is known as reward-to-variability ratio. Asset allocation is the allotment of funds across different types of assets with varying expected risk and return levels. Capital allocation is the allotment of funds between risk-free assets, such as certain Treasury securities, and risky assets, such as equities. The standard deviation of the Treasury bill is 0% Sharpe Ratio: Help investors understand the return of an investment compared to its risk. The ratio is the average return earned in excess of the risk-free rate per unit volatility or total risk The greater the value of the sharpe ratio, the more attractive the risk-adjusted return Sharpe Ratio = Rp – Rf / σp Excess Return over risk free return / SD of returns Rp = Return of portfolio Rf = risk-free rate Sigma p = standard deviation of the portfolio’s excess return Co-efficient of Variation ( Standard Deviation / Mean ) Lower the better What is Co-efficient of Variation? Risk taken to earn 1 percentage return is the Co-efficient of return Jensen’s Alpha Information Ratio Although compared funds may be different in nature, the IR standardizes the returns by dividing the difference in their performances, known as their expected active return, by their tracking error IR = (Portfolio Return – Benchmark Return) / Tracking Error where: IR=Information ratio Portfolio Return=Portfolio return for period Benchmark Return=Return on fund used as benchmark Tracking Error=Standard deviation of difference between portfolio and benchmark returns The information ratio (IR) is a measurement of portfolio returns above the returns of a benchmark, usually an index such as the S&P 500, to the volatility of those returns The information ratio is used to evaluate the skill of a portfolio manager at generating returns in excess of a given benchmark A higher IR result implies a better portfolio manager who's achieving a higher return in excess of the benchmark, given the risk taken ER of portfolio = ER of risk-free asset x weight of risk-free asset + ER of risky asset x (1- weight of riskfree asset) Risk of portfolio = weight of risky asset x standard deviation of risky asset Capital Market Line is a special case of the CAL where the portfolio of risky assets is the market portfolio. Volatility is a total risk. E (Rp) = Rf + sigma p * ( E (Rm)- Rf/ sigma m) The risk free return Rf represents the reward for waiting. (Rm- Rf) / Sigma m i.e., the excess return earned per unit of risk or standard deviation Expected Return = price of time + price of risk* amount of risk The required rate of return on a Portfolio. = risk free rate + portfolio risk premium Portfolio risk premium = standard deviation of the portfolio * market risk premium Rp = rf + σp* (Rm- rf/ σm) where: Rp = Portfolio return rf = Risk free rate Rm = Market return σp = Standard deviation of portfolio returns σm = Standard deviation of market returns It’s standard deviation. Treynor ratio Reward per unit of systemic risk Treynor ratio best used with well-diversified portfolios. Because in those portfolios nonsystematic risk has been diversified away. the CML is used to express the risk and return relationship for diversified portfolios only, whereas the SML can be used to show the relationship between risk and return for any asset. But CML uses standard deviation as the risk measure whereas the SML uses beta Jensen’s Measure P rP r f P ( rM r f ) Only considers the systemic risk Information Ratio = Average Alpha of the portfolio / Standard Deviation of the Alpha The information ratio (IR) is a measurement of portfolio returns beyond the returns of a benchmark, usually an index, compared to the volatility of those returns. The benchmark used is typically an index that represents the market or a particular sector or industry. IR = (Portfolio Return – Benchmark Return) / Tracking Error Tracking Error = Take the standard deviation of the difference between the portfolio returns and the index returns. M squared measure = SR * σbenchmark + (rf) Performance Attribution Contribution of Asset Allocation to performance = market return * ( Actual Weight – Benchmark Weight) Contribution of Selection to Total performance = portfolio weight* ( Actual return – Index return ) Security Market Line is derived from Capital Market Line Required rate of return on Security i = risk free rate of return + risk premium to invest in the risky security i In CML the risk is defined as total risk and is measured by standard deviation In SML the risk is defined as systemic risk and is measured by Beta Measure of risk in the CML is the standard deviation of returns (total risk) The risk measure in the SML is systemic risk or beta Optimal Risky Portfolios 1. Capital allocation between the risky portfolio and risk-free asset 2. Asset allocation across broad asset classes 3. Security selection of individual assets within each asset class Market risk remains even after extensive diversification aka systemic or non-diversifiable risk Firm-specific risk: Risk that can be eliminated by diversification aka diversifiable or non-systemic risk Portfolio risk depends on the correlation between the returns of the assets in the portfolio Covariance and the correlation coefficient provide a measure of the way returns of two assets vary Portfolio Performance Evaluation
