# 8-4 Alternative Theories â€‹

The CAPM pictures investors solely concerned with the level of uncertainty of their future wealth, but this is a too simplistic view.

## Arbitrage Pricing Theory â€‹

Arbitrage Pricing Theory

**APT** does not ask which portfolios are efficient. It starts assuming that each stock's return depends partly on pervasive macroeconomic influences or *factors* and partly on *noise*. The return is assumed to obey the relationship:

**The theory does not say what the factors are.**

a factor could be for example the oil price. the **b** term is how related the factor is to the stock price.

- coca cola price is less related to oil price than exxon mobile.

finding expected return for a stock.

- Identify a reasonably short list of macroeconomic factors that could affect the stock's returns.
- Estimate the risk premium on each of these factors.
- Measure the sensitivity of each stock to these factors.

### Risk in APT â€‹

For any individual stock there are two sources of risk:

- the risk that stems from the
**factors**. (something negative happens that affects the entire market)**cannot be eliminated by diversification**.

- risk that stems from
**company specific events.****diversification eliminates this risk.**

the expected **risk premium** on a stock is affected by factor or macroeconomic risk it is not affected by specific risk.

Arbitrage pricing theory states that the expected risk premium on a stock should depend on the expected risk premium associated with each factor and the stock's sensitivity to each of the factors.

If you plug in a value of zero for every b in the formula the expected risk premium is 0. A diversified portfolio that is constructed to have zero sensitivity to each macroeconomic factor is essentially risk free ("arbitrage") profit. (

*either by holding or shorting the portfolio based on it's return*)A diversified portfolio that is constructed to have exposure to say factor 1, will offer a risk premium, which will vary in direct proportion to the portfolio's sensitivity to that factor.

### The Three Factor Model â€‹

Three Factor Model

The three factor model is a shortcut on APT.

It already has three factors identified. return formula:

Book to Market

The book to market ratio compares a company's book value to its market value. The book value = value of it's assets - the value of the liabilities. Market value = the market price of one of its shares multiplied by the number of shares outstanding.

Factor | Measured By | estimated risk premium |
---|---|---|

Market factor | Return on market index minus risk free interest rate | 7% |

Size factor | Return on small-firm stocks minus return on large-firm stocks | 3.2% |

book to market factor | Return on high book to market ratio stocks minus return on low book-to-market stocks | 4.9% |

finding expected return for a stock.

- âœ… Identify a reasonably short list of macroeconomic factors that could affect the stock's returns.
- âœ… Estimate the risk premium on each of these factors.
- listed in the table, they can be re-calculated with historical data.
- done by finding the average of the yearly differences

- Measure the sensitivity of each stock to these factors.
- Some stocks are more sensitive than others to the three factors.
- it's up to the investor to find an estimate of these sensitivities.

**Examples:**

- an increase of
`1%`

in the return on the book-to-market factor*reduces*computer stocks by`0.21%`

- when value stocks (high book to market) outperform growth stocks (low book to market), computer stocks perform relatively badly.
- gas and oil stocks do relatively well

this model is not widely used in practice.