See question 2008 #4 B. The answer states that the Sharpe ratio of a portfolio that consists of 106.5% of a corner portfolio 4 has the same Sharpe Ratio as the unlevered portfolio (0.51), although no math is shown. How is it that the use of leverage does not create additional risk per unit of return? Under that logic, why wouldn’t you just lever to the hilt?
Buckhead Wrote: ------------------------------------------------------- > See question 2008 #4 B. > > The answer states that the Sharpe ratio of a > portfolio that consists of 106.5% of a corner > portfolio 4 has the same Sharpe Ratio as the > unlevered portfolio (0.51), although no math is > shown. > > How is it that the use of leverage does not create > additional risk per unit of return? > > Under that logic, why wouldn’t you just lever to > the hilt? The assumption is that you can borrow and lend at the risk free rate. This does not generally hold in real life, it is just for the sake of the model. The point is that if you borrow money at the risk free rate and invest it in your portfolio you will increase the standard deviation and risk adjusted return proportionately, so the sharpe ratio will stay the same.
just imagine the CAL . the fact that you borrow makes you move along the CAL - to the right. the sharpe ratio is the slope of CAL. in your case you don’t change the slope, you just move along CAL - the effect will be to increase expected return and increase expected risk, but the ration between the two will remain the same
gentlemen thanks for your answers. That makes perfect book sense and zero common sense, which means they must be right for CFA.