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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.)
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.
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.
- 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
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)
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
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
Portfolio of n risky assets
- E(rP) = ∑wiE(ri)
- σP2 = ∑wi2σi2 + ∑∑wiwjσij
Minimum Variance Portfolio
w1 = (σ22 - σ1σ2ρ) / (σ12 + σ22 - 2σ1σ2ρ)
Optimal Portfolio of Risky Assets
- w1 = (RP1σ22 - RP2σ12) / (RP1σ22 + RP2σ12 - (RP1 + RP2)σ12)
- where RPi = E(ri) - rf
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 → ∞