ECO349H5 Chap.4 Risk Premia and Equity Valuation
Risk Premia and Equity Valuation
Value depends on the state
A risky cash flow is valuable not only because of its average size but because of the states in which it arrives. Consumption-based pricing attaches greater weight to payoffs delivered when consumption is scarce and marginal utility is high. A claim that performs in bad aggregate states supplies insurance and can command a high price even when its expected payoff is modest.
A good-state claim may require a higher expected return.
Build price from state weights
The stochastic discount factor combines time preference with the change in marginal utility between today and the payoff date. Asset price is the expected product of that factor and the future payoff. Write the state table with probability, payoff and discount factor in separate columns.
Multiplying expected payoff by an average discount factor generally fails when the two variables covary.
The covariance form makes the economics visible. Price equals the discounted expected payoff plus a covariance adjustment. Positive covariance between payoff and the pricing factor raises value because the claim pays when resources are especially useful.
Negative covariance lowers insurance value and raises the compensation investors require. Check the sign against the state story rather than memorizing a premium rule in isolation.
Distinguish risk measures
Variance and standard deviation measure total dispersion. Equilibrium risk compensation depends on exposure to aggregate conditions, because idiosyncratic variation can be diversified across many claims.
CAPM expresses this distinction through beta, the covariance of a security’s return with the market relative to market variance. A high-volatility security need not have the highest beta when most of its movement is claim-specific.
Alpha is a model-relative residual, not automatic proof of skill or mispricing. It can reflect sampling error, an omitted risk factor or an unstable benchmark.
When interpreting an estimated return relation, name the model, the horizon and the relevant systematic exposure. When answering a theoretical problem, do not import an empirical beta unless the question supplies the needed mapping.
Value a growing dividend stream
The Gordon model prices next period’s dividend divided by the required return minus the constant growth rate.
The next dividend, not the dividend just paid, belongs in the numerator. The required return must exceed growth for the standard infinite-series expression to converge. Check that inequality before calculating; a small denominator makes the answer extremely sensitive to either input.
A higher growth rate raises value only if the required return is held fixed.
A higher required return lowers value when expected dividends are unchanged. In practice, the two can move together because stronger growth prospects may also change exposure or discount rates. A complete comparative-static answer states which assumption moves, which are held constant and why the denominator changes.
Connect valuation and premia
Price and expected return are two views of the same claim.
A lower price for a fixed payoff schedule implies a higher expected return, but the economic reason may be weak cash-flow expectations, high systematic risk or both. Decompose the question before applying a formula. If only discounting changes, hold dividends fixed.
If operating prospects change, revise the cash-flow path before inferring a premium.
Revision should combine one two-state pricing exercise, one covariance-sign explanation and one Gordon sensitivity table. For each answer, add a unit check and a sentence about assumptions. Then ask whether the result describes total risk, priced exposure or an equity multiple.
This disciplined labelling prevents volatility, beta, required return and growth from becoming interchangeable words.
What this chapter covers
- 01
Stochastic discount factor
- 02
Equity premium
- 03
Covariance
- 04
CAPM beta
- 05
Gordon growth
Worked example · free
Value a dividend with constant growth
- 1Verify that the required return exceeds the perpetual dividend growth rate.
- 3Insert next period's dividend and calculate the return-growth denominator.
Key terms
- Systematic Risk
- Systematic Risk is exposure to aggregate states that diversification cannot remove.
- Gordon Growth
- Gordon Growth values a perpetually growing cash flow under constant return and growth assumptions.
Risk Premia and Equity Valuation FAQ
Why is covariance central to risk premia?
A payoff that is low when marginal utility is high provides poor insurance and must offer compensation. Variance alone cannot show whether the claim performs badly in economically valuable states.
Is beta the same as volatility?
No. Beta measures exposure to a market benchmark, while volatility includes both systematic and idiosyncratic movement. Diversification can reduce the latter without eliminating aggregate exposure.
Does a high price-earnings ratio prove a bubble?
No. Higher expected growth or a lower required return can raise the ratio. A bubble argument must compare the price with a defensible cash-flow and discount-rate model and acknowledge uncertainty in those inputs.
Exam move
Price one two-state claim, interpret covariance signs, and recompute Gordon value under separate growth and discount shocks.
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