# Relaxing Assumptions of CAPM

**Short Sales Disallowed**

- CAPM assumes that unlimited short selling is allowed
- Relaxing this assumption does not have too much impact on CAPM because in CAPM framework, investors hold the market portfolio in equilibrium and in this situation no investor will sell the security short

**Riskless Lending and Borrowing**

- CAPM assumes that investors can borrow and lend unlimited amounts at risk free rate
- Case 1 â€“ No risk free rate is available
- In this case a zero beta portfolio is used in CAPM in place of risk free rate
- Since there are multiple zero beta portfolios are available, the correct zero beta portfolio will be the one which has smallest total risk

- Case 2 â€“ Risk free rate is available to lend but no risk free rate is available to borrow
- Risk free assets are available, e.g. US Treasury Bills, so risk free lending is possible but risk free borrowing is not available to many borrowers
- In this case, the SML will change in shape shown in the graph on next slide

- Case 1 â€“ No risk free rate is available

- All the risky portfolios that are formed as a combination of market portfolio and the zero beta portfolio have a required return given on the line r
_{z }TM

# Personal Taxes

- Another assumption of capital asset pricing model is that it ignores personal taxes
- The model is assumes that the investor is indifferent towards receiving income from capital gains or dividends. This assumption is not very realistic
- Investors judge the performance of the portfolio on after tax basis. This is the reason, that relaxing this assumption is very important
- To relax this limitation, CAPM equation is adjusted to include dividend yield on the market portfolio and the stock

# Non-marketable Assets

- One of the assumptions of CAPM is that all the assets are easily marketable
- In reality, every investors holds some assets that are not easily marketable
- Assets might be non marketable because buying or selling them might involve huge transaction cost and there are certain non financial factors also which might affect the marketability of
- the asset
- To relax this assumption, CAPM equation is broken down into two parts to include both marketable and non marketable assets

# Heterogeneous Expectations

- CAPM model assumes that all the investors have homogenous expectations
- In reality, each investor has different expectations
- Investors have different utility functions
- It is difficult to relax this assumption in CAPM
- Beta is an adequate risk measure and equilibrium model leads to linear relationship between expected return and beta, similar to more simple forms of CAPM

# Non-Price Taking Behavior

- CAPM model assumes that all the investors are price takers
- However in reality, there are few large investors which are price affecters
- Price affecter's actions increase utility
- The end result is still consistent with the simple forms of CAPM