# Asset Pricing

(very much work in progress - feel free to contribute)

Financial markets serve several purposes:

1. Allowing investors to shift consumption in time
2. Allowing the transfer of risk between different investors
3. Moving capital from those who have it to those who can use it productively

Asset pricing is the study of how financial assets are priced.

Financial assets include several varieties:

1. Debt
2. Equities
3. Hybrids
4. Derivatives

Whatever the particular variety, we can think of financial assets simply as the right to a future cash flow stream and/or physical asset. All types of asset, e.g., debt, equity, etc., can be reduced to a stream of cash flows that can be valued.

When valuing a stream of cash flows we need to consider these things:

• Time value of money
• Riskiness of the cash flows
• Expected value of the cash flows

For debt, asset pricing is relatively simple, as cash flows to the owner are contractually fixed. For example, the holder of a 20-year US government bond with a face value of $100 and a coupon of 5% paid annual can expect (with high certainty) to be paid$5 a year for the next 20 years, with \$100 to be returned at the end of 20 years. The value of the bond is the present value of the future cash flows. If the required rate of return is r=3% a year, then the value is: ${\frac {5}{r}}*(1-{\frac {1}{(1+r)^{20}}})+{\frac {100}{(1+r)^{20}}}=129.75$ .

Although debt security can have predictable cash flow in the future (e.g., assuming we are talking about fixed rate debt security) there still is an element of uncertainty because expected rate of return is likely to change over the above mentioned 20 years time period. This would change the present value of the debt security depending on the assumption or derivation of the rate of return that applies to each individual time period. This adds interest rate risk component to the debt security valuation.

If the debt issuer is not a "AAA" rated sovereign state then we cannot assume the cash flow is guaranteed. This adds a credit risk component. Debt securities issued by all entities are rated by investment grade rating services (e.g.,. Moody's, Standard & Poor's) and this can be used to determine the required rate of return to account for the risk, which will the impact the valuation of the debt security.

For equities, asset pricing is more difficult as future cash flows are uncertain, and vary with both economic conditions and the fortune of the company. We need to project future expected cash flows, and also determine the expected return of the stock. The estimated expected return of the stock is based on an estimate of how risky the cash flows are. We can decompose risk into a) common factor risk and b) idiosyncratic risk. The latter can be diversified away in a portfolio, so earns no return premium. The former cannot be diversified away, so earns a risk premium.

Suggested reading: Cochrane, Asset Pricing http://www.pupress.princeton.edu/titles/7836.html

Sharpe, Investors and Markets http://www.stanford.edu/~wfsharpe/art/princeton/pup1.pdf