1.2.BKM Ch 07

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  1. Two general types of risk
    • Market risk: a.k.a. systematic, non-diversifiable. Arises from uncertainty in the general economy (business cycle, interest rates, etc.)
    • Firm-specific risk: a.k.a. non-systematic, unique, diversifiable. Arises from factors directly attributable to a firm's operations (R&D, personel, etc.)
  2. Hedge Asset
    A hedge asset has negative correlation with the other assets in the portfolio, so that such asset will be particularly effective in reducing total risk.
  3. Efficient portfolio exception
    • In special cases where investors have restrictions, it is possible that a single asset my be efficient risk portfolio.
    • Example: asset w/ highest E(r) will be a frontier portfolio if can not short sale.
  4. Separation Property
    • Portfolio selection consists of 2 independent tasks:
    • 1. Determination of optimal risky portfolio
    • 2. Allocation of the complete portfolio (risk-free vs risky)
    • The degree of risk aversion of the client comes into play only in the selection of the desired point along the CAL
  5. Asset Allocation vs Security Selection
    • Demand for sophisticated security selection has increased due to need and ability to save for the future
    • Amateurs are at a disadvantage due to widening spectrum of financial markets/instruments
    • Strong economies of scale result when sophisticated investment analysis is conducted (expertise, international)
  6. Minimum-variance frontier of risky assets
    • Graph of the lowest possible variances that can be attained for a given E(rP)
    • Then determine CAL with the highest reward-to-variability ration tangent to the efficient frontier
  7. Risk Pooling vs Risk Sharing
    • Risk pooling: it appears that when firm sells more policies, σ decreases, reflecting risk reduction. This is false as increasing the bundle of policies does not make for diversification.
    • What explains the ins industry is Risk sharing, which is the distribution of a fixed amount of risk among many investors
  8. Portfolio of n risky assets
    • E(rP) = ∑wiE(ri)
    • σP2 = ∑wi2σi2 + ∑∑wiwjσij
  9. Minimum Variance Portfolio
    w1 = (σ22 - σ1σ2ρ) / (σ12 + σ22 - 2σ1σ2ρ)
  10. Optimal Portfolio of Risky Assets
    • w1 = (RP1σ22 - RP2σ12) / (RP1σ22 + RP2σ12 - (RP1 + RP212)
    • where RPi = E(ri) - rf
  11. Power of diversification
    • Assume a PF is constructed using N assets each w/ wi = 1/N
    • σP2 = (1/N)∑(σi2/N) + (N - 1/N)∑∑(σij/N(N-1))
    • σP2 = (1/N)(avg variance) + (N - 1/N)(avg cov)
    • where the first term → 0 as N → ∞

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1.2.BKM Ch 07
2011-02-08 02:36:16

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