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FINS5513 The Market Portfolio and Capital Market Line

创建日期：2024-05-30 17:32:23

所属分类：金融Finance

标签： FINS5513

The Market Portfolio and Capital Market Line

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FINS5513 Lecture 3

CAPM and SIM
2❑ 3.1 General Equilibrium: Derivation of the CAPM
➢ Capital Asset Pricing Model (CAPM) Assumptions
➢ The Market Portfolio and Capital Market Line
➢ Derivation of the CAPM
❑ 3.2 Interpreting the CAPM
➢ Beta
➢ Security Market Line
➢ Applications and Extensions of the CAPM
❑ 3.3 The Single Index Model (SIM)
➢ Limitations of the CAPM
➢ SIM
➢ Alpha
➢ Decomposition of the total risk
Lecture Outline
3.1 General
Equilibrium: Derivation
of the CAPM
FINS5513
4Capital Asset Pricing Model
(CAPM) Assumptions
FINS5513
5❑ Markowitz established modern portfolio theory through important contributions in 1952
and 1959
❑ Based on this work, Sharpe, Lintner, Mossin and others published papers between 1964-
1966 which collectively became known as the Capital Asset Pricing Model (CAPM)
❑ CAPM is a model for deriving expected returns on risky assets under equilibrium
conditions
❑ CAPM is derived under a general equilibrium framework.The assumptions under
which the CAPM is derived simplify the world with regard to:
➢ Individual behaviour
➢ Market structure
❑ The CAPM assumptions are often considered to be stylised and not reflective of reality
Capital Asset Pricing Model (CAPM) Evolution
6❑ Individual behaviour
➢ Investors are rational, mean-variance optimisers (as per Markowitz)
➢ Investors are price takers - no investor is large enough to influence equilibrium prices
➢ Investors common planning horizon is a single period
➢ Investors have homogeneous expectations on the statistical properties of all assets (i.e.
same expected returns and covariances and all relevant information is publicly
available)
❑ Market structure
➢ Investors can borrow and lend at a common risk-free rate with no borrowing constraints
➢ All assets are publicly held and traded on public exchanges
➢ Perfect capital markets - there are no financial frictions such as short selling
constraints, transaction costs, taxes etc
❑ Under these assumptions, all investors derive the same efficient frontier, CAL, and ∗
CAPM Assumptions
7The Market Portfolio and
Capital Market Line
FINS5513
8❑ The foundations of the CAPM come from Markowitz and separation theorem:
➢ Sharpe began with the question “What if everyone is optimising a la Markowitz?”
❑ Under separation theorem, EVERY rational investor invests along the CAL, regardless of
risk aversion
➢ because all portfolio combinations on the CAL have the highest Sharpe ratio
❑ Therefore, in market equilibrium all investors hold the same optimal risky portfolio ∗
❑ If, in equilibrium, all investors are holding the same ∗, this must be the market portfolio
, and must comprise all assets
➢ The weight of each asset in is the asset’s market value divided by the total value of

➢ Every investor holds some portion of this market portfolio
❑ Since ∗ is the market portfolio , also has the highest possible Sharpe ratio
Separation Theorem Implications
9❑ The rational way to increase return (and risk) is to invest more in (rather than deviating
from and buying risky assets in different weightings to their weightings in )
❑ Since every investor invests in , the common CAL associated with is called the Capital
Market Line (CML)
The Capital Market Line
❑ The CML is equivalent to the optimal CAL. It is
the aggregation of EVERY investors’ CAL
which are all the same
❑ is equivalent to ∗. It is the aggregation of
EVERY investor’s optimal risky portfolio ∗
which are all the same
❑ Every investor invests along the CML.
Movements along the CML represent different
allocations between and the risk-free asset
10
❑ An investor can implement an entirely passive strategy requiring no security analysis
❑ Requires two assets:
➢ Risk-free: short-term T-Bills or money market mutual fund
➢ Risky: mutual fund or an ETF tracking a broad based market index (eg the S&P500)
❑ Then, draw a line joining the two assets. This represents is a practical version of the CML
❑ Example: According to BKM Table 6.7, the U.S. equity market returned 11.72% with a
standard deviation of 20.36% (assume for simplicity this represents the Market portfolio
although it is only a proxy) and 1-month T-bills (the risk-free asset) returned 3.38% between
1926 and 2018.
a) Draw the Capital Market Line. What is the slope of this line and what does it represent?
b) Aggressive Investor A and Conservative Investor C target maximum portfolio risk of 25%
and 14% respectively. For investors A and C: calculate their allocation to the equity market
(∗) and T-bills (1 − ∗), the expected return on their complete portfolio (∗), the Sharpe
ratio of their complete portfolio, and their implied risk aversion coefficient .

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