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Two general types of risk
 Market risk: a.k.a. systematic, nondiversifiable. Arises from uncertainty in the general economy (business cycle, interest rates, etc.)
 Firmspecific risk: a.k.a. nonsystematic, unique, diversifiable. Arises from factors directly attributable to a firm's operations (R&D, personel, etc.)

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.

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.

Separation Property
 Portfolio selection consists of 2 independent tasks:
 1. Determination of optimal risky portfolio
 2. Allocation of the complete portfolio (riskfree 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)

Minimumvariance frontier of risky assets
 Graph of the lowest possible variances that can be attained for a given E(r_{P})
 Then determine CAL with the highest rewardtovariability 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(r_{P}) = ∑w_{i}E(r_{i})
 σ_{P}^{2 }= ∑w_{i}^{2}σ_{i}^{2} + ∑∑w_{i}wjσ_{ij}

Minimum Variance Portfolio
w_{1} = (σ_{2}^{2}  σ_{1}σ_{2}ρ) / (σ_{1}^{2} + σ_{2}^{2}  2σ_{1}σ_{2}ρ)

Optimal Portfolio of Risky Assets
 w_{1} = (RP_{1}σ_{2}^{2}  RP_{2}σ_{12}) / (RP_{1}σ_{2}^{2} + RP_{2}σ_{1}^{2}  (RP_{1} + RP_{2})σ_{12})
 where RP_{i} = E(r_{i})  r_{f}

Power of diversification
 Assume a PF is constructed using N assets each w/ w_{i} = 1/N
 σ_{P}^{2} = (1/N)∑(σ_{i}^{2}/N) + (N  1/N)∑∑(σ_{ij}/N(N1))
 σ_{P}^{2} = (1/N)(avg variance) + (N  1/N)(avg cov)
 where the first term → 0 as N → ∞

