复旦大学：《投资学讲义》（英文版） Cherpter 3 capital allocation

INVESTMENTS Capital allocation between the risk asset and the iskfreeeisget

INVESTMENTS Capital allocation between the risky Capital allocation between the risky asset and the risk asset and the risk-free asset free asset Chapter 3 Chapter 3

INVESTMENTS The choice of proportion in safe asset and proportion in risky asset a Most institutional investors follows top- down analysis---The first part is asset allocation and the next part is security selection decision

INVESTMENTS Capital allocation 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- ree porrol1oS---excirrple Total wealth 300.000 a90,000 in money market The remaining is in risky assets---113 400 in ibm and 96. 600 in gm a The risky portfolio is 54%in IBM, and 46% in GM a The complete portfolio is 30% in risk-free asset; 70% in risky portfolio

INVESTMENTS Capital allocation across risky and risk Capital allocation across risky and risk- free portfolios free portfolios---example 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 a Weight in risky portfolio is y, in risk-free asset Is l-y a Return on the risky portfolio is Rp, return on risky free asset is Rr, Suppose E(Rn)=15%0n=22%,R=7% a Portfolio return is R=yR,+(1-y)R

INVESTMENTS Portfolio of one risky asset and one risk Portfolio of one risky asset and one risk- free asset 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 E(Rp ) =15%,σ p = 22%,Rf = 7% C p Rf R = yR + (1− y)

INVESTMENTS corrIne The expectation of the portfolio return is E(R)=yER, )+(1-yR R +ye(r-RI 7+y(15-7) Standard deviation of the portfolio return is c= yo,=22y ■ We can also write E(RC)=R+yLE(Rp)-R R+[E(R2)-R +—0

INVESTMENTS continued continued „ The expectation of the portfolio return is „ Standard deviation of the portfolio return is „ We can also write y y C p σ = σ = 22 ( ) ( ) 7 (15 7 ) [ ( ) ] ( 1 ) = + − = + − = + − y R y E R R E R yE R y R f p f C p f C p f p C f C f p f R E R R E R R y E R R σ σ σ 22 8 7 [ ( ) ] ( ) [ ( ) ] = + = + − = + −

INVESTMENTS pItal allocation lire CAL=capital allocation line E(R)-R=8%0 R=7% =22% The figure graphs the investment opportunity set

INVESTMENTS Capital allocation line Capital allocation line CAL=capital allocation line σ p = 22% E(Rp ) − Rf = 8% Rf = 7% E(Rp ) =15% The figure graphs the investment opportunity set

INVESTMENTS Reward-to-yariability ratio The slope of the graph is called reward-to variability ratio: E(R )-R S a Can the reward-to-variability ratio of an 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?

INVESTMENTS Reward -to -variability ratio 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 E R p R f S σ

INVESTMENTS What about if borrowing and lending rate air If lending rate is still 7% but borrowing rate is 9% CAL=capital E(R)=15% allocation line R=9% E(R)-R=8%0 R=7% 0=22% The figure graphs the investment opportunity set

INVESTMENTS What about if borrowing and lending What about if borrowing and lending rate are different? rate are different? CAL=capital allocation line σ p = 22% E(Rp ) − Rf = 8% Rf = 7% E(Rp ) =15% The figure graphs the investment opportunity set. If lending rate is still 7%, but borrowing rate is 9% = 9% B Rf

INVESTMENTS Passive strategies: the capital market 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 a We call the cal provided by one-month T-bills and a broad index of common stocks the capital market line( Cml)

INVESTMENTS Passive strategies: the capital market 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 isk tolerance and asset allocation a With utility function U=E(R)-005402 a We choose best allocation to the risky asset y, to maximize our utilities

INVESTMENTS Risk tolerance and asset allocation Risk tolerance and asset allocation „ With utility function „ We choose best allocation to the risky asset, y , to maximize our utilities. 2 U = E ( R ) − 0.005 A σ