AFM273 Chapter Notes - Chapter 12: Risk-Free Interest Rate, Market Portfolio, Risk Premium

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C12: The Equity Cost of Capital
The equity cost of capital
Cost of capital is the best expected return available in the market for investments of similar
Can calculate return easily if the 3 parameters are present
o Risk free rate
o Market risk premium
o Beta
Investors require a risk premium comparable to what they would earn taking the same
market risk through an investment in the market portfolio
The Market Portfolio
Constructing the market portfolio
o Market portfolio represents total supply of securities
To properly replicate each stock should be weighted as it would be to the effect
of the actual market
o Investment in each security, I, is proportional to its market capitalization
The total market value of its outstanding share
o Mvi = (number of shares of i outstanding) x (price per share of i)
o Portfolio weight of each security is as follows
o Portfolio having its weights in proportion to market values is called a value-weighted
Also an equal-ownership portfolio
Holds equal fraction of shares to each security in the portfolio
Also a passive portfolio
Little trading is required
Market indexes
o Common practice to use large market indexes to substitute as a market portfolio
This is like S&P 500, TSX 60
o Dow Jones is price-weighted not value weighted
Holds an equal number of shares of each stock independent of their size
Not representative of the market
o Value-weighted portfolios remain value weighted even with price shifts since the
proportions remain the exact same.
Market proxy
Belief that the index represents the return of a true market portfolio
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o Index funds
Mutual funds that invest in the large indexes
o ETFs
Security that trades directly on an exchange like a stock but represents
ownership in a portfolio of stocks
The Market Risk Premium
Estimating market risk premium E[Rmkt] -Rf requires estimating both of its components
Determining the risk free interest rate
o T-bills and longer government bonds are both default risk free
If their maturity does not match our desired investment horizon they will be
subject to interest rate risk
o To get the risk free rate usually use long term 10-30 year government bonds
The historical risk premium
o One estimate method is the historical average excess return for the market index over
the risk-free rate
This requires many years of data to get good estimate because of large standard
of error
o Overtime market premium has shrunk
Do to the greater sharing of risk, more investors
Mutual funds and ETFS have greatly reduced diversification costs
These may have led to lower market risk so less premium
o 2 issues
Need large data set
Backward looking, may not follow true with the future
Fundamental approach
o Can forecast cash flows for firms contained in market index, we can estimate the
market return by finding the discount rate that is consistent with the current level of the
Essentially, if we can estimate free cash flows, we can isolate for the discount
rate that would give us the current index level (price) and then use that to find
the market return
o This type of procedure usually gives an estimated market risk premium of 3-5%
Estimating Beta
Using historical returns
o Beta usually estimated using the stock's historical sensitivity to the market
o Beta is easy to find online but can vary a lot
Typically they are 2-5 years' worth of weekly/monthly return data
o Characteristic line
Line of best fit in the scatterplot of betas
Identifying the characteristic line
o On a scatterplot put all the points of returns over a period of time
Line of best fit is the characteristic line
o Beta corresponds to the slope of the characteristic line in the plot of the security's
excess returns versus the market excess returns
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