# Risk And Return Essay

449 words - 2 pages

Holding Period Return
HPR=(Ending price-Beginning price+Dividend during period one)/(Beginning price)=(P_1-P_0+D_1)/P_0
Dividend Yield: % return from dividends
Expected Return and Standard Deviation
E(r)=∑_s▒〖p_s r_s 〗
σ=√(∑_s▒〖p_s (r_s-E(r))〗^2 )

Expected end-of-year value of the investment =Dividend+Ending Price
Arithmetic and Geometric Averages
Arithmetic Mean (AM) =(∑▒HPR)/N
Better predictor of future performance
Geometric Mean (GM) = π(1+HPR) )^(1/N)-1
Better measure of past performance
GM < AM

Sharpe Ratio
Sharpe Ratio for Portfolios =(Excess Return)/(SD of Excess Return)=(R_i-R_f)/(σ(R_i-R_f))
Measure the attraction of an investment portfolio by comparing its reward (risk premium) and risk (SD)
Excess ...view middle of the document...

5Aσ^2

U=E(r)-0.005*A*σ^2
Utility value is used to facilitate cross asset comparison
Higher values are assigned to portfolios with more attractive risk-return portfolios
Utility score of risky portfolios = certainty equivalent rate of return
Portfolio is desirable only if certainty equivalent return > risk-free alternative
Certainty equivalent rate of return = the rate that risk-free investments need to offer to provide the same utility score as the risky portfolio
Undominated Assets
Dictated by the investor’s personal tradeoff between risk and return

Indifference Curve
Connects all portfolio points with the same utility value
Investor is indifferent between different assets on curve
Changes in Utility Changes in Level of Risk Averse

Step 2: Portfolio Return and Risk
Portfolio Return
r_p=W_1r1+W_2r2
Portfolio Risk
Variance=〖σ_p〗^2=〖W_1〗^2 〖σ_1〗^2+〖W_2〗^2 〖σ_2〗^2+2W_1 W_2 Cov(r_1,r_2)
=〖W_1〗^2 〖σ_1〗^2+〖W_2〗^2 〖σ_2〗^2+2W_1 W_2 σ_1 σ_2 ρ_12

Effect of Correlation on Portfolio Risk

*Perfectly positively correlated assets: Portfolio s.d is the average of the s.d of the assets in the portfolio

Diversification and Portfolio Risk
Market risk (common risk)
Systematic or nondiversifiable
Firm-specific risk
Diversifiable or nonsystematic

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