Lecture notes
FINANCIAL ECONOMICS NOTES
- Module
- (BS3389)
- Institution
- Aston University, Birmingham (Aston)
IN DEPTH AND DETAILED NOTES ON FINANCIAL ECONOMICS
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Financial economics – Part Beta TheoryPortfolio choice
- An application of the von Neumann-Morgenstern utility theory
- A set of normative methods → how to choose how much to invest and at which assets
- It assumes:
o Rational decision makers
o Uncertainty of outcomes
o A single investment decision
- Portfolio construction → how should an investor combine risky assets
o Risk Exposure → how much risk an investor should take
o Can take a top down or bottom up approach
Time value of money
- The PV ➔ prices
- Interest rates ➔ also known as liquidity premium
- Assume: you have £100 and deposit it for two years at 10% p.a. How much do you have after?
o Simple interest = principle*rate*time = 100*0.1*2 = 20 ➔ 20 + 100 = £120
o Compound ineptest = P x (1 + r)t ➔ 100 x (1 + 0.1)2 = £121
Gross vs Log returns
- The principle of participation → if a risky asset has a positive excess return (R-Rf), then irrespective of the
level of risk aversion, investment in this asset should be positive
o Positive excess return → positive investment
- If the excess return is 0, irrespective of the level of risk aversion, investment in this asset should be 0 (non-
participation)
- Key assumption: you can only choose between 1 risky asset and 1 safe (risk free) asset
- When returns are small → i.e. what if we have a risk (i.e. risky asset) with small reward (positive excess return)
o Then we can write y = kµ + ε
▪ k = is a small positive scalar
▪ µ = the mean return of y
▪ ε = the zero mean component of risk
o following the Arrow-Pratt methodology, the optimal pound investment θ*(k) we get, irrespective of
the utility function is given by: 𝜽∗ (𝒌) = [𝑬(𝒚) ∕ 𝑽𝒂𝒓(𝒚)] ⋅ [𝟏 ∕ 𝑨(𝒘𝟎 )]
o Expressed in terms of the share of wealth: 𝒂∗ (𝒌) = [𝑬(𝒚) ∕ 𝑽𝒂𝒓(𝒚)] ⋅ [𝟏 ∕ 𝑹(𝒘𝟎 )]
o 1 – a = % in the risk free asset; a = % in the risky asset
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