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**Unformatted text preview: **Corporate Finance II (FINC 2012) Lecture CAPITAL ASSET PRICING MODEL Andrew Lepone Finance Discipline University of Sydney Market Equilibrium If :- everyone is a mean-variance optimiser; - there are no transaction costs ie frictionless capital markets;- there exists a unique risk-free rate for borrowing & lending;- all investors have homogeneous (identical) expectations or beliefs about the distribution of returns offered by all assets; All investors will perceive the same efficient set One-Fund Theorem : ⇒ all investors will try to hold some combination of the risk-free asset and a single fund of risky assets. (Mix of these is likely to vary across individuals in accordance to their risk preference, but every individual will hold a combination of the risk-free asset and a single, risky one fund ). If every investor purchases the same fund of risky assets, what must this portfolio or fund be? The fund must be equal to the market portfolio . Market portfolio is the summation of assets; in the context of equity securities it is the totality of all stocks. If every investor buys just one fund, and their purchases add up to the market, then that one fund must be the market as well! That single fund must contain shares of every stock in proportion to that stock’s representation in the entire market. For market to be in equilibrium, we require a set of market- clearing prices. All assets must be held. ⇒ existence of equilibrium requires that all prices be adjusted so that excess demand for any asset will be zero. This market clearing condition implies that equilibrium is not attained until the single-tangency portfolio M, which all investors (with homogeneous expectations) try to combine with risk-free asset, is a portfolio in which all assets are held according to their market value or capitalisation weights. If V i is the market value of the i th asset, then the percentage of wealth held in each asset is equal to the ratio of the market value of the i th asset to the market value of all assets. Mathematically: ∑ = = N i i i i V V w 1 Market equilibrium is not reached until the tangency portfolio, M, is the market portfolio. Capital Market Line • Given the single efficient fund of risky assets is the market portfolio, then the efficient set is a straight line emanating from the risk-free rate passing through the market portfolio, M . Capital Market Line (CML) Shows the linear relation between the expected return and risk (as measured by the standard deviation) for efficient assets or portfolio of assets. Equation of CML: ) ( ) ( ] [ ] [ p m f m f p r r r r E r r E σ σ - + = E(r p ) σ (r p ) Efficient Set r f M σ (r M ) E(r M ) ) ) ( ) ( ] [ ] [ p m f m f p r r r r E r r E σ σ - + = • Slope of CML ≡ - ) ( ] [ m f m r r r E σ ≡ ‘price of risk’ • CML ⇒ as risk ↑ → expected return ↑ Individual utility maximisation in a world with capital markets....

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