INVESTMENTS Capital allocation between the risky asset and the risk-free asset Chapter 3 INVESTMENTS Capital allocation ? The choice of proportion in safe asset and proportion in risky asset; ? Most institutional investors follows top- down analysis---The first part is asset allocation and the next part is security selection decision. INVESTMENTS Capital allocation across risky and risk- free portfolios---example ? Total wealth 300,000; ? 90,000 in money market; ? The remaining is in risky assets---113,400 in IBM and 96,600 in GM ? The risky portfolio is 54% in IBM, and 46% in GM; ? The complete portfolio is 30% in risk-free asset; 70% in risky portfolio. INVESTMENTS Portfolio of one risky asset and one risk- free asset ? Weight in risky portfolio is y, in risk-free asset is 1-y; ? Return on the risky portfolio is Rp, return on risky free asset is Rf; ? Suppose ? Portfolio return is %7%,22%,15)( === fpp RRE σ fpC RyyRR )1( ?+= INVESTMENTS continued ? The expectation of the portfolio return is ? Standard deviation of the portfolio return is ? We can also write yy pC 22== σσ ( ) ( ) )715(7 ])([ )1( ?+= ?+= ?+= y RREyR RyRyERE fpf fpC C fp p C f fpfC RRER RREyRRE σ σ σ 22 8 7 ])([ ])([)( += ?+= ?+= INVESTMENTS Capital allocation line CAL=capital allocation line %22= p σ %8)( =? fp RRE %7= f R %15)( = p RE The figure graphs the investment opportunity set. INVESTMENTS Reward-to-variability ratio ? The slope of the graph is called reward-to- variability ratio: ? Can the reward-to-variability ratio of any combination of the risky asset and the risk- free asset be different from the ratio for the risky asset taken alone, which in this case is 0.36? 22 8 )( = ? = p fp RRE S σ INVESTMENTS What about if borrowing and lending rate are different? CAL=capital allocation line %22= p σ %8)( =? fp RRE %7= f R %15)( = p RE The figure graphs the investment opportunity set. If lending rate is still 7%, but borrowing rate is 9% %9= B f R INVESTMENTS Passive strategies: the capital market line ? The CAL is derived with the risky portfolio and risk-free portfolio; ? When constructing the risky portfolio with no analysis, we follow a passive investment strategy; ? Usually, the passive risky portfolio is a large index, for example S&P500; ? We call the CAL provided by one-month T-bills and a broad index of common stocks the capital market line(CML). INVESTMENTS Risk tolerance and asset allocation ? With utility function ? We choose best allocation to the risky asset, y , to maximize our utilities. 2 005.0)( σAREU ?=