1.2.BKM Ch 07

• 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.

• 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

• 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)

• Graph of the lowest possible variances that can be attained for a given E(r_P)
• Then determine CAL with the highest reward-to-variability ration tangent to the efficient frontier

• 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

• E(r_P) = ∑w_iE(r_i)
• σ_P² = ∑w_i²σ_i² + ∑∑w_iwjσ_ij

w₁ = (σ₂² - σ₁σ₂ρ) / (σ₁² + σ₂² - 2σ₁σ₂ρ)

• w₁ = (RP₁σ₂² - RP₂σ₁₂) / (RP₁σ₂² + RP₂σ₁² - (RP₁ + RP₂)σ₁₂)
• where RP_i = E(r_i) - r_f

• Assume a PF is constructed using N assets each w/ w_i = 1/N
• σ_P² = (1/N)∑(σ_i²/N) + (N - 1/N)∑∑(σ_ij/N(N-1))
• σ_P² = (1/N)(avg variance) + (N - 1/N)(avg cov)
• where the first term → 0 as N → ∞