S8 Capital Assets Pricing Model (CAPM)

S8 Capital Assets Pricing Model (CAPM) Assumptions of CAPM 1. Investors are price takers 2. Financial markets are perfect 3. Investors have homogenous investment horizons and expectations on return , variance and convariance of returns 4. All investors are risk averse and rational mean-variance optimisers 5. Investors can borrow and lend at the same risk free rate 6. Risky assets consist of publicly traded financial assets such as stocks and bonds

Capital Market Line (CML) & Sharpe Ratio  

Investment opportunity set – all attainable portfolios of risky assets with the risk return combination within the min variance set. Efficient frontier – line that shows risk-return combination of portfolios of risky assets that offer largest level of expected return for given level of risk

𝐸(𝑟𝑝 ) = 𝑟𝑓 +  

𝐸(𝑟𝑚 ) − 𝑟𝑓 ×𝜎𝑝 𝜎𝑚

“beat the market”  achieve portfolio lying above CML Any portfolio below CML is inferior to the market portfolio

Sharpe’s Ratio (slope of CML) 𝑆𝑝 = 

𝐸(𝑟𝑝 ) − 𝑟𝑓 𝜎𝑝

“beaten market” if sharpe ratio of portfolio > sharpe ratio of market portfolio.

1

Beta1 

Beta2 of a risky asset shows the relative amount of risk the asset contributes to the market portfolio.

Calculating asset Beta 𝛽𝐶𝐵𝐴 =

𝑐𝑜𝑣(𝑟𝐶𝐵𝐴 , 𝑟𝑀 ) 2 𝜎𝑚

Sum of individual asset beta = 1 𝑛

∑ 𝑤𝑖 𝛽𝑖 = 1 𝑖=1

Beta of market portfolio = 1 𝛽𝑚=

𝑐𝑜𝑣(𝑟𝑀 , 𝑟𝑀 ) 𝜎2𝑀

=

𝜎2𝑀 𝜎2𝑀

=1

Security Market Line (SML) SML equation 𝐸(𝑟𝑖 ) = 𝑟𝑓 + 𝛽𝑖 [𝐸(𝑟𝑚 ) − 𝑟𝑓 ]

1

See p106 for derivation

2

Risk CBA contributes to market portfolio = 𝑤𝐶𝐵𝐴 𝑐𝑜𝑣(𝑟𝐶𝐵𝐴 , 𝑟𝑀 ) 𝑤𝐶𝐵𝐴 Proportion of risk that is contributed by CBA = 𝑐𝑜𝑣(𝑟𝐶𝐵𝐴 , 𝑟𝑀 )× 2 = 𝑤𝐶𝐵𝐴 𝛽𝐶𝐵𝐴 𝜎𝑀

2