# 1.3.BKM Ch 08

 Drawbacks of the Markowitz Model Requires a huge # of estimates (cov)Does not provide guideline to forecast RPErrors in estimation of σij can lead to nonsensical results Index Models Decomposes a security's return into systematic and firm-specific componentAs valid as the assumption of normality of the rates of returnTo the extent that short-term returns are well approximated by normal distributions, index models can be used to select optimal portfolios nearly as accurately as the Markowitz algorithmAssumption: the rate of return of a broad index is a valid proxy for the common macroeconomic factor Index Model Regression Equation Ri(t) = αi + βiRM(t) + ei(t) The Single-Index-Model Input List RP on the selected index (eg. S&P 500)σ of the selected indexn sets of estimates of (a) β coefficients, (b) stock residual variances, and (c) α values Single Index Model ri = E(ri) + βim + eiσi2 = βi2σm2 + σ2(ei)σP2 = βP2σm2 + ∑wiσ2(ei)Cov(ri, rj) = βiβjσm2The index model is estimated by applying regression analysis to xs rates of return. β = slope, α = intercept Is the Index Model inferior to the Full-Covariance Model? To add anouther index, we need both a forecast or the risk prem and estimates of βUsing the full covariance matrix invokes estimation risk of thousands of termsEven if the full Markowitz is better in principle, it is very possible that cumulative effect of so many estimation error will results in an inferior PF. 8 steps to determine weights of a portfolio 1. Calculate initial weights based on α/σ2(ei)2. Scale weights so that ∑wi = 13. Compute αP4. Compute σ2(eA) (residual variance of PF)5. wA° = [αA/σ2(eA)]/[E(RM)/σM2]6. Calculate βA7. Adjust weights to account for βwA* = wA°/[1 + (1 - βA)wA°]8. Compute E(rOPF) and σOPF Evolution of β over time As time goes by, β → 1.0As firms grow, they diversify and therefore their β approaches the mkt βMerrill adjusted β = (2/3)E(β) + (1/3)(1.0) AuthorExam9 ID58676 Card Set1.3.BKM Ch 08 DescriptionBKM Updated2011-02-08T02:36:39Z Show Answers