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**Unformatted text preview: **where r n is return in each of n subperiods e.g. credit card that charge 3% monthly: APR = 12*3% = 36% EAR = (1 + 3%) 12 – 1 = 42.6% 8 Comparing Rates of Return For risky investments: Holding-period return (HPR) = Price increase + dividends Initial price Expected return = E[HPR] Standard deviation = Risk premium = E[HPR] – Risk-free rate = 9 Sharpe Ratio Sharpe ratio = Risk premium Std. dev. first proposed by William Sharpe measures the “risk-weighted” excess return = 10 Value at Risk (VaR) Value-at-Risk = quantile of the return distribution = measure of loss under extreme market conditions typically 5% quantile (or 5 th percentile) is used Interpretation: the loss on an investment will be larger than the 5% VaR with 5% probability important in risk management systems to limit the maximum loss Example: VaR at Goldman Sachs for daily trading losses was $250m in 2010 (up from $125m in 2007)...

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