Central Bank of Egypt Performance Measurement Tools
Central Bank of Egypt Rate of return: Calculate NAV: Source : world Bank
Central Bank of Egypt Performance & Cash Flows • 2 types of cash flows: ØExternal Cash Flows : Contributions into or withdrawals from the portfolio Ø Internal Cash Flows : Cash flows associated with purchases, sales, and coupon payments are within the portfolio
Central Bank of Egypt Various rates of return formulas: • Dietz Mid-Point: assuming cash flows occur at the middle of month. • Modified Dietz calculate “weighting factors for each flow CF* Source : world Bank
Central Bank of Egypt Buy & Hold Return vs. Total Return • The buy/hold return will not necessarily equal the portfolio return from the changes in market value: • Securities held in the portfolio may change between the beginning and ending dates due to trading activity • Holdings of existing securities may have changed over the period due to trading activity Source : world Bank
Central Bank of Egypt Linking & annualizing Return • Geometric Linking: calculate returns over multiple periods. Total Return = (1 + Rt) * (1 + Rt+1) *…. . * (1 + Rn) • Annualizing Return: to compare returns with different holding periods on a consistent basis (HP more than 1 year) Numbers Holding period cumulative of years in return HP Source : world Bank
Central Bank of Egypt Relative Performance • Why measure Relative performance? – Monitor the value added of the investment decisions relative to a benchmark: • value-added of active versus passive management • value-added of each strategy/manager Source : world Bank
Central Bank of Egypt Other measurement tools
Central Bank of Egypt 1 -Treynor Portfolio Performance Measure A risk-adjusted measure of return that divides portfolio's excess return by its beta. The Treynor Measure is given by • The Treynor Measure is defined using the average rate of return fo portfolio p and the risk-free asset. • Because it adjusts returns based on systematic risk, it is the relevant performance measure when evaluating diversified portfolio held in separately or in combination with other portfolios.
2 -Sharpe Measure Central Bank of Egypt • Similar to the Treynor measure, but uses the total risk of the portfolio, not just the systematic risk. • The Sharpe Ratio is given by • The larger the measure the better, as the portfolio earned a higher excess return per unit of total risk.
Central Bank of Egypt 2 -Sharpe Measure • It adjusts returns for total portfolio risk, as opposed to only systematic risk as in the Treynor Measure. • Thus, an implicit assumption of the Sharpe ratio is that the portfolio is not fully diversified, nor will it be combined with other diversified portfolios. • It is relevant for performance evaluation when comparing mutually exclusive portfolios. • Sharpe originally called it the "reward-to-variability" ratio, before others started calling it the Sharpe Ratio.
Central Bank of Egypt 3 -Jensen’s Alpha • Alpha is a risk-adjusted measure of superior performance • This measure adjusts for the systematic risk of the portfolio. • Positive alpha signals superior risk-adjusted returns, and that the manager is good at selecting stocks or predicting market turning points. • Unlike the Sharpe Ratio, Jensen’s method does not consider the ability of the manager to diversify, as it is only accounts for systematic risk.
Central Bank of Egypt 4 -Information Ratio • Measures excess returns relative to a benchmark portfolio. • Sharpe Ratio is the special case where the benchmark equals the risk-free asset. • Risk is measured as the standard deviation of the excess return (Recall that this is the Tracking Error) • For an actively managed portfolio, we may want to maximize the excess return per unit of nonsystematic risk we are bearing.
Central Bank of Egypt Case study & Thank You
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