Portfolio Diversification and
Supporting Financial Institutions
CLASS NOTES:
Portfolio can help hardship
Part of risk management
Math:
Capital asset and pricing model
Correction of assets = portfolio (à portfolio management)
Return vs. variance
n independent assets
Sigma = Std dev of return
r = expected return
Square root rule
Sigma_portfolio = sigma/square(n)
Equally Weighted
r_portfolio = r
Two Asset Case: n = 2 not independent
Asset1 r1= E(return1) Sigma1 = Std dev(return1)
Asset 2 r2 = E(return2) Sigma2 = Std dev(return2)
Cov(r1, r2) = Sigma12
X1 = in asset 1
1-X1 in asset 2
X2= 1-X1
Portfolio Exp return
r = SUM(xiri) = x1rx + x2r2 = x1r1+(1-x1)r2
x1 = (r-r2)/(r1-r2)
Riskless asset
Sigma_f = 0: straight line
Tangency portfolio
The tangency portfolio combines the optimal combination of risky assets with a risk-free asset.
Mutual fund theorem
Mutual fund theorem
Capital asset pricing model
CAPm
Tobin, Sharpe, Lintner, Markowls
Assume everyone is rational, holds tangency portfolio.
Tangency portfolio = Actual market portfolio
r1=rf + Bi*(rm-rf)
rm: expected ret on market portfolio
Financial modeling has been researched and invented for part of risk management. The result from these equations can be useful information for decision making of investors whether they should invest. Efficient frontier (Harry Markowitz and others) which is a concept in modern portfolio theory has been explained mainly. The figure of Standard [Deviation vs Expected Returns] is explained. Top straight line of the hyperbola is called “efficient Frontier” and it has optimum returns for the investment under the given set of risks.
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