1. Cost of Capital: Capital Asset Pricing Model (CAPM) and Weighted Average Cost of Capital (WACC)
Magdalena Partac

2. Lesson Plan: 1) Modern Portfolio Theory;
Previous Lecture
Today
Knowledge and Understanding
1) Modern Portfolio Theory;
1) Capital Asset Pricing Model (CAPM)
2) Portfolio diversification (2 assets);
2) Portfolio Diversification (3 assets)
3) Active and Passive investment strategies.
3) Weighted Average Cost of Capital
Intellectual, practical, affective and transferable skills
1) Solution to the Trial Test 2;
1) Task 1 CAPM
2) Introduction to Bloomberg.
2) Task 2 Business and Financial Risks

3. 𝜎 𝑝 2 = ( 𝑤 𝐴 𝜎 𝐴 ) 2 + (𝑤 𝐵 𝜎 𝐵 ) 2 +2( 𝑤 𝐴 𝜎 𝐴 )( 𝑤 𝐵 𝜎 𝐵 ) 𝜌 𝐴𝐵
Diversification
Variance of the Portfolio:
𝜎 𝑝 2 = ( 𝑤 𝐴 𝜎 𝐴 ) 2 + (𝑤 𝐵 𝜎 𝐵 ) 2 +2( 𝑤 𝐴 𝜎 𝐴 )( 𝑤 𝐵 𝜎 𝐵 ) 𝜌 𝐴𝐵
Where 𝜌 𝐴𝐵 is the correlation coefficient between assets.
With 3 assets:
𝜎 𝑝 2 = ( 𝑤 𝐴 𝜎 𝐴 ) 2 + (𝑤 𝐵 𝜎 𝐵 ) 2 + ( 𝑤 𝐶 𝜎 𝐶 ) 𝑤 𝐴 𝜎 𝐴 𝑤 𝐵 𝜎 𝐵 𝜌 𝐴𝐵 +2( 𝑤 𝐴 𝜎 𝐴 )( 𝑤 𝐶 𝜎 𝐶 ) 𝜌 𝐴𝐶 + 2( 𝑤 𝐵 𝜎 𝐵 )( 𝑤 𝐶 𝜎 𝐶 ) 𝜌 𝐵𝐶

4. Correlation Coefficient
𝜌 𝐴𝐵 = 𝜌 𝑅 𝐴 𝑅 𝐵 = 𝜎 𝑅 𝐴 𝑅 𝐵 ( 𝜎 𝑅 𝐴 )( 𝜎 𝑅 𝐵 ) Correlation coefficient falls between -1 (perfectly negative) and +1 (perfectly positive), i.e. -1 ≤𝜌 𝐴𝐵 ≤ 1. Where 𝜎 𝑅 𝐴 𝑅 𝐵 is covariance between A and B: 𝜎 𝑅 𝐴 𝑅 𝐵 =𝐶𝑂𝑉 𝑅 𝐴 𝑅 𝐵 = 𝑠=1 𝑆 𝑝 (𝑠) [ 𝑟 𝐴,𝑠 −𝐸 𝑟 𝐴 ][ 𝑟 𝐵,𝑠 −𝐸 𝑟 𝐵 ] ; Where 𝑟 𝐴,𝑠 is the return on Asset A in state/scenario s; 𝑟 𝐵,𝑆 is the return on asset B in state/scenario s. 𝐸 𝑟 𝐴 , 𝐸 𝑟 𝐵 are the expected returns on asset A and B, respectively. Covariance can take any values, and it measures the relationships between two assets by taking into account how the assets behave in each state/scenario.

5. Cost of Capital
In investment appraisal methods we discussed the k – the management’s discount rate or management’s target return.
Today we will determine this “k”

6. The CAPM (Capital Asset Pricing Model)
The CAPM was originally developed by Treynor, Sharpe, Linter, and Mossin in the early 1960s and refined further later on;
The CAPM is a theory about the way assets are priced in relation to
their risk exposure;
The model predicts risk-return relationship among all the risky assets;
It was derived using principles of diversification;
It was developed based on some hypothetical behavioral assumptions on securities markets and investor.

7. Six assumptions of CAPM
1) Individual investors cannot affect prices; i.e. price takers so market sets the price.
2) All investors plan for a single-period investment horizon.
3) Investors form portfolios from a universe of publicly traded financial assets and have access to unlimited risk-free borrowing or lending opportunities.
4) Frictionless market: investors pay neither taxes nor transaction costs on trades in securities.
5) Investors attempt to construct efficient frontier portfolios (Rational mean- variance optimizers).
6) All investors analyze securities in the same way and share the same economic view of the world (! homogeneous expectations).

8. Further assumptions
To derive the CAPM, we also assume that a risk-free asset exists (risk-free rate = rf ) and investors can buy or sell it.
In a capital market that reflects these assumptions, all investors would face the same efficient frontier (or the same minimum variance set) as they have identical expectations.

9. `Market Portfolio M'
In equilibrium all investors will hold a (hypothetical) market portfolio (M) that includes every security available to investors in a given market in amounts proportional to their market values.
The proportion of each stock in the market portfolios equals the market value of the stock (price per share times the number of shares outstanding) divided by the total market value of all stocks.

10. Resulting equilibrium conditions: (2) optimal risky portfolio
M will be on the efficient frontier.
It will be the optimal risky portfolio, the tangency point of the capital allocation line (CAL) to the efficient frontier.
The capital market line extends from rf through the point M and beyond.
As a result, the CML is also the best attainable CAL.
All investors hold M as their optimal risky portfolio.
Investors differ only in the amount invested in M as compared to the amount invested in the risk-free asset.

11. Capital Market Line (CML)

12. CML slope and market risk premium
The slope of the capital market line is sometimes termed as price of risk as it indicates how much extra risk has to be borne in order to obtain an extra unit of expected return.

13. Investment Policy: active or passive
The capital market line is the capital allocation line that results from using a passive investment strategy that treats a market index portfolio such as the FTSE100 as the risky assets.
(I)Active (`Informed'): Trying to secure better than average performance ,but (!) costly.
(II) Passive ("uninformed") are low-cost ways of obtaining well-diversified portfolios with performance that will reflect that of the broad stock market:
Based on the premise that securities are fairly priced and avoids the
costs involved in undertaking security analysis.
It involves trying to get average returns rather than do better than the
market.

14. Resulting equilibrium conditions: (3) Beta coefficient
The risk premium on individual assets will be proportional to the risk premium on M and to the beta coefficient of the security on the market portfolio.
The beta measures the extent to which returns on the stock respond to the returns on M.
The sensitivity of a security's returns to the systematic (non-diversifiable) factor is called BETA.

15. BETA
Measures the sensitivity of a security's returns to the systematic or market factor. It is given by:
𝛽 𝑖 = 𝑅𝑒𝑡𝑢𝑟𝑛 𝑐𝑜𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑠𝑒𝑐𝑢𝑟𝑖𝑡𝑦 𝑖 𝑤𝑖𝑡ℎ 𝑚𝑎𝑟𝑘𝑒𝑡 𝑅𝑒𝑡𝑢𝑟𝑛 𝑣𝑎𝑟𝑖𝑎𝑛𝑐𝑒 𝑜𝑓 𝑡ℎ𝑒 𝑚𝑎𝑟𝑘𝑒𝑡 =
= 𝜎 𝑟 𝑖 𝑟 𝑀 𝜎 𝑟 𝑀 2

16. Quantifying the CAPM: expected return-beta relationships
The rate of return of an asset i’s is given by that of the risk-free rate plus the asset i's systematic risk measure ( 𝛽 𝑖 ) times the risk premium of the
benchmark market portfolio. In other words:
𝐸 𝑟 𝑖 = 𝑟 𝑓 + 𝛽 𝑖 [ 𝐸 (𝑟 𝑀 ) − 𝑟 𝑓 ],
The beta measures how returns on the stock respond to the market return M.

17. Task 1 CAPM
Suppose that the risk premium on the market portfolio is estimated at 11% and we estimate a beta for Intel to be 1.2 (Intel = 1:2). The risk premium predicted for the stock is therefore 1.2 times the market risk premium or 1.2×11% = 13.2%. If the T-bill rate was 4%, the expected rate of return for Intel would be?
17.2

18. Securities Market Line
The SML is the graphical representation of the expected return-beta relationship of the CAPM.
Its slope is the risk premium of the market portfolio.

19. Investment decision using SML
The SML provides a benchmark for evaluating an investment project.
Given the risk of an investment as measured by its beta, the SML provides the required rate of return that will compensate investors for the risk of that investment, as well as for the time value of money.
`Fairly priced' assets will plot exactly on the SML.

20. Meaning of SML and disequilibrium
Whenever CAPM holds, all securities must lie on the SML in market equilibrium.
Underpriced stocks will plot above the SML.
Overpriced stocks will plot below the SML.
The difference between the fair and actual expected rate of return on a stock is called alpha (α, or Jensen’s alpha):
𝛼 𝐽 = 𝐸 ( 𝑟 𝑖 ) −[ 𝑟 𝑓 + 𝛽 𝑖 𝐸 (𝑟 𝑀 ) − 𝑟 𝑓 ]

21. Determining k using CAPM
With CAPM, management can determine the appropriate cost of capital provided that the firm is all or mostly equity financed. This is often
referred to as The Equity Cost of Capital (Cost of Equity, 𝐾 𝑒 ).
The firms can raise capital either by issuing shares or selling debts.
Therefore the cost of capital depends from cost of equity and cost of debt

22. The total cost of capital
In a mix debt/equity combination, the cash flows generated from the projects can be used to pay BOTH the bondholders and equity holders.
Weighted Average Cost of Capital:
𝑊𝐴𝐶𝐶=𝑊𝑒×𝐾𝑒+𝑊𝑑× 𝐾 𝑑 ;
We – weight of equity;
Wd- weight of debt;
Ke- cost of equity (CAPM);
Kd-cost of debt.
When there are market frictions such as taxes, then the cost of capital structure will change since taxes provide tax deductions on interest payments which reduces the cost of debt.

23. Task 2: open Seminar 6 task on Canvas+
15 min ?
Calculations
Discussion

24. Thank you for your attention