1.3.BKM Ch 08

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1.3.BKM Ch 08
2011-02-07 21:36:39

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  1. Drawbacks of the Markowitz Model
    • Requires a huge # of estimates (cov)
    • Does not provide guideline to forecast RP
    • Errors in estimation of σij can lead to nonsensical results
  2. Index Models
    • Decomposes a security's return into systematic and firm-specific component
    • As valid as the assumption of normality of the rates of return
    • To 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 algorithm
    • Assumption: the rate of return of a broad index is a valid proxy for the common macroeconomic factor
  3. Index Model Regression Equation
    Ri(t) = αi + βiRM(t) + ei(t)
  4. The Single-Index-Model Input List
    • RP on the selected index (eg. S&P 500)
    • σ of the selected index
    • n sets of estimates of (a) β coefficients, (b) stock residual variances, and (c) α values
  5. Single Index Model
    • ri = E(ri) + βim + ei
    • σi2 = βi2σm2 + σ2(ei)
    • σP2 = βP2σm2 + ∑wiσ2(ei)
    • Cov(ri, rj) = βiβjσm2
    • The index model is estimated by applying regression analysis to xs rates of return. β = slope, α = intercept
  6. 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 β
    • Using the full covariance matrix invokes estimation risk of thousands of terms
    • Even 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.
  7. 8 steps to determine weights of a portfolio
    • 1. Calculate initial weights based on α/σ2(ei)
    • 2. Scale weights so that ∑wi = 1
    • 3. Compute αP
    • 4. Compute σ2(eA) (residual variance of PF)
    • 5. wA° = [αA2(eA)]/[E(RM)/σM2]
    • 6. Calculate βA
    • 7. Adjust weights to account for β
    • wA* = wA°/[1 + (1 - βA)wA°]
    • 8. Compute E(rOPF) and σOPF
  8. Evolution of β over time
    • As time goes by, β → 1.0
    • As firms grow, they diversify and therefore their β approaches the mkt β
    • Merrill adjusted β = (2/3)E(β) + (1/3)(1.0)

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