fa04 - introduction to asset pricing models
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FA04 - Introduction to Asset Pricing ModelsTRANSCRIPT
Introduction to
Asset Pricing Models
Capital Asset Pricing Model
Introduction to Asset Pricing Models2
Model to price all risky assets based on existing portfolio
theory (e.g. Risk Aversion, Return Maximization)
Gives the required rate of return for any given risky asset.
Assumptions
Introduction to Asset Pricing Models3
All investors are Markowitz Efficient Investors.
All investors can borrow or lend at the risk free rate.
All investors have homogenous expectations.
All investors have the same investment time horizon.
All investments are infinitely divisible.
No tax and transaction costs in buy/sell.
No inflation or change in interest rates.
Capital markets are in equilibrium.
Risk Free Asset
Introduction to Asset Pricing Models4
Risky Asset = Asset with uncertain returns.
Risk-Free Asset = Asset with σ = 0
Thus, for any investment, minimum return should be at least
equal to the risk-free rate.
In modelling, this is usually the 365-day T-Bill rate.
Risk-Free Asset in a Risky Portfolio
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Expected Return
Standard Deviation
𝐸 𝑅𝑃𝑜𝑟𝑡 = 𝑊𝑅𝐹 𝑅𝐹𝑅 + 1 −𝑊𝑅𝐹 𝐸(𝑅𝑖)
𝜎 = (𝑤𝑎𝜎𝑎)2 + (𝑤𝑏𝜎𝑏)
2 + 2𝜌𝑤𝑎𝑤𝑏𝜎𝑎𝜎𝑏
𝜎 = (𝑤𝑅𝐹𝜎𝑅𝐹)2 + [(1 − 𝑤𝑅𝐹)𝜎𝑖]
2 + 2𝜌𝑤𝑅𝐹𝑤𝑖𝜎𝑅𝐹𝜎𝑖
𝜎 = [(1 − 𝑤𝑅𝐹)𝜎𝑖]2 = (1 − 𝑤𝑅𝐹)𝜎𝑖
𝑆𝑖𝑛𝑐𝑒 𝜎𝑅𝐹 = 0,
Risk-Free Asset in a Risky Portfolio
Introduction to Asset Pricing Models6
Linear combinations of risk-free and risky asset portfolio.
Point M = point of tangency with portfolio M.
𝐸 𝑅𝑃𝑜𝑟𝑡 = 0 𝑅𝐹𝑅 + 1 𝐸 𝑅𝑀 = 𝐸(𝑅𝑀)
𝐸 𝑅𝑃𝑜𝑟𝑡 =1
2𝑅𝐹𝑅 +
1
2𝐸(𝑅𝑀)
Risk-Free Asset in a Risky Portfolio
Introduction to Asset Pricing Models7
What if you want a return higher than M ?
Higher than D, but with the same level of risk.
𝐸 𝑅𝑃𝑜𝑟𝑡 = −0.5 𝑅𝐹𝑅 + [1 − −0.5 ]𝐸(𝑅𝑖)
𝐸 𝑅𝑃𝑜𝑟𝑡 = −0.5 𝑅𝐹𝑅 + 1.5𝐸(𝑅𝑖)
Risk-Free Asset in a Risky Portfolio
Introduction to Asset Pricing Models8
New efficient frontier = Capital Market Line (CML)
Market Portfolio
Introduction to Asset Pricing Models9
Includes all risky assets - Completely Diversified Portfolio Stocks – Local and International
Bonds
Options
Real Estate
Physical Assets – antiques, coins, gold, art, etc.
Complete Diversification takes away all unsystematic (diversifiable and unique) risk.
Systematic Risk = caused by macroeconomic variables.
All assets are in proportion to their market value.
Security Market Line (SML)
Introduction to Asset Pricing Models10
Given that the Market Portfolio is the ideal and completely
diversified portfolio, an individual asset’s risk can be attributed
to its variability, or covariance, with the market portfolio.
If asset is riskier than market portfolio, then a higher return is expected.
If asset is less risky than market portfolio, lower return is expected.
Capital Asset Pricing Model (CAPM)
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Beta – standardized measure of systematic risk.
1 = perfectly correlated with the market portfolio.
> 1 = more volatile than market portfolio.
< 1 = less volatile than market portfolio.
𝐸 𝑅𝑖 = 𝑅𝐹𝑅 +𝑅𝑀 − 𝑅𝐹𝑅
𝜎𝑀2 𝐶𝑜𝑣𝑖,𝑚
𝐸 𝑅𝑖 = 𝑅𝐹𝑅 +𝐶𝑜𝑣𝑖,𝑚
𝜎𝑀2 (𝑅𝑀 − 𝑅𝐹𝑅)
𝐸 𝑅𝑖 = 𝑅𝐹𝑅 + 𝛽(𝑅𝑀 − 𝑅𝐹𝑅)
Required vs Estimated Returns
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Required – ideal return given level of risk as indicated by
CAPM Model.
If RFR = 6% and Market Rate of Return = 12%, compute for
the required returns of each stock and determine whether
the stock is properly, under, or over valued.
Stock Beta Estimated Return
A 0.70 10.0%
B 1.00 6.2%
C 1.15 21.2%
D 1.40 3.3%
E -0.30 8.0%