standard deviation

Standard deviation

HOLDING PERIOD RETURN a)

BREAKDOWN Holding Period Return FORMULA INTO FORMULAS FOR DIVIDEND YIELD AND CAPITAL GAINS YIELD

DIVIDEND YIELD FORMULA b)

CAPITAL GAINS FORMULA c)

FISHER EFFECT EX ANTE AND EX POST FORMULAS

FISHER EFFECT IS USED TO FIND ___?

REAL RISK FREE RATE OF INTEREST

REAL RATE OF INTEREST FORMULA

standard deviation

standard deviation

expected return of the portfolio

Further, suppose that 40% of the portfolio is invested in Stock X and 60% in Stock Y. In order to calculate the standard deviation of the portfolio, first we need to calculate the expected returns of both stocks:

E[Rx]=.21×(−2%)+.46×11%+.33×26%=13.22%E[Rx]=.21×(−2%)+.46×11%+.33×26%=13.22%

E[Ry]=.21×3%+.46×13%+.33×14%=11.23%E[Ry]=.21×3%+.46×13%+.33×14%=11.23%

The expected return on a portfolio is simply the weighted average of the returns on the individual assets. As such, the expected return on our example portfolio is:

E[Rp]=.4×13.22%+.6×11.23%=12%E[Rp]=.4×13.22%+.6×11.23%=12%

Next, calculate the standard deviations of each stock:

σx=√.21(−2%−13.22%)2+.46(11%−13.22%)2+.33(26%−13.22%)2=10.24%σx=.21(−2%−13.22%)2+.46(11%−13.22%)2+.33(26%−13.22%)2=10.24%

σy=√.21(3%−11.23%)2+.46(13%−11.23%)2+.33(14%−11.23%)2=4.27%σy=.21(3%−11.23%)2+.46(13%−11.23%)2+.33(14%−11.23%)2=4.27%

The covariance of the two stocks are:

COVx,y=.21×(−2%−13.22%)×(3%−11.23%)+.46×(11%−13.22%)×(13%−11.23%)+.33×(26%−13.22%)×(14%−11.23%)=36.18%COVx,y=.21×(−2%−13.22%)×(3%−11.23%)+.46×(11%−13.22%)×(13%−11.23%)+.33×(26%−13.22%)×(14%−11.23%)=36.18%

Given the standard deviation of each individual asset and the covariance of the two assets, the correlation coefficient of these stocks is:

ϱa,b=36.18%10.24%×4.27%=.82ϱa,b=36.18%10.24%×4.27%=.82

Therefore, the standard deviation of the portfolio is (using the correlation coefficient):

σp=√(.4)2×(10.24%)2+(.6)2×(4.27%)2+2×.4×.6×.8256×10.24%×4.27%=6.38%

beta definition

measures how correlated the firm's returns are with the returns of the entire market's returns

KAPM EQUATION

RISK FREE RATE =

BUILD UP METHOD FORMULA

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A company that you are analyzing has a beta of 1. The expected market return is 14.5%. According to the CAPM, what is the expected return of this company?

GKL and Associates has a beta of 1.1. The market risk premium is expected to be 8% and the risk free rate is 3.5%. According to the CAPM, what is the expected return for GKL?

Suppose a company has a beta of .86. Also, assume the market risk premium is 10% and the expected return on the market is 13.5%. According to the CAPM, what is the expected return for this company?

(Required rate of return using CAPM) Compute Bowling Avenue Inc.’s required rate of return given a beta of .9, risk free rate of 3.25%, and the average market return of 9%.

(Capital asset pricing model) Compute Fine Co.’s required rate of return given a beta of 1.5, risk free rate of 5%, and a market premium of 4%.