Ch. 5: Risk/Return: • As compounding periods increase, EAR gets bigger than APR; since EAR uses compounding, EAR gets bigger • 3 determinants of real interest rates: supply of funds from households, demand of funds from corporations, gov. action • Taxed on nominal income, reducing your real return • When inflation increases people need higher nominal rates to cancel out the effect, so nominal increases w/ inflation to make sure that the real rate stays the same • Risk premium = what you expect; excess return = amount over Rf that you actually got • Right skewed dist. has too high SD, positive fluctuations are favorable but still factored as risk; longer time series increase accuracy of mean estimates, increased observation freq. increases accuracy of SD • Sharpe Ratio: Numerator increases directly w/ time, denominator increases w/ Square root of time since its SD and variance increases w/ time Ch. 6: Risky Assets: • You have 100% of your money to invest in combo of risky and risk free, but you can lever up: sell off the amount of T-bills and invest more than w=1 in risky; but you can’t sell bonds (borrow) at Rf, it would be higher. So, the slope of the CAL after you exceed 100% weight in P would be flatter because the Sharpe Ratio numerator you’re subtracting your borrowing rate, not the risk-free rate Ch. 7: Optimal Risky Portfolio: • Unless the two risky assets are perfectly correlated, then you get a lesser variance by combining the two = diversification • Choose the combo of 2 assets that has the highest Sharpe Ratio, then pick how much of that combo to invest in your overall based on the utility function formula Ch. 8: Index Models: • Index model: returns of securities normal distribution based on common macro factor with the equation on the other sheet Ch. 9: CAPM: • Assumptions: mean/var. optimizers, same inputs lists, all investments publicly traded, no taxes/transaction costs, borrow at Rf • If everyone has same frontier to choose from, going to choose the best one, aggregated, that would be the market portfolio so the CAL line that people face is the same as the CML for whole market – don’t have to do security analysis the MKT is good • Within market portfolio, measure how one stock (GE) affects the whole portfolio; variance measure by seeing how it covaries with other stocks in portfolio (whole market) =Cov(r mkt, r GE). Now you see how good the stock (reward-volatility ratio) by dividing its expected return by the covariance w market. The market portfolio overall has reward-volatility of E(r mkt) / Var(mkt). These two equations should equal each other b/c the stocks weighted average should equal the market’s. Can rearrange to solve for the return on GE. When rearranging you get Cov(r GE, r mkt)/Var(mkt), which is just Beta. Totally rearranged, you get the CAPM formula. Beta • Zero Beta CAPM: Smaller risk premium and flatter SML, instead of subtracting out Rf to get the risk premium,
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