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Lay out the drivers of asset prices and account for the theory behind risk premiums attached to factors.

FRM® Part II · Risk Management and Investment Management · Factor Theory · FRM2.IM.1.a

The idea

An asset's price is the present value of its expected cash flows, so it moves when expected cash flows change or when the discount rate changes. The discount rate is the risk-free rate plus a risk premium. Factor theory says a premium is paid only for exposure to systematic factors. Systematic factors are broad sources of risk such as economic growth, inflation, real rates and market liquidity. Idiosyncratic risk earns no premium, because it diversifies away. A factor earns a positive premium when assets exposed to it lose value in bad times, when an extra unit of wealth is most valuable. Assets that pay off in bad times work as insurance and can earn less than the risk-free rate. Explanations are rational (compensation for bad-times risk), behavioral (investor biases) or structural (institutional constraints). The common error is rewarding total volatility. Premiums follow covariance with bad times.

A practice question

From the question bank, with the reason each wrong option is wrong.

In a standard asset pricing framework, the price of a risky asset is best described as:

  1. the present value of its expected cash flows, discounted at the risk-free rate plus a premium for the risk borne - correct
  2. the present value of its expected cash flows, discounted at the risk-free rate aloneWhy not: Omits the risk premium; discounting at the risk-free rate is risk-neutral valuation and overprices risky assets.
  3. the undiscounted sum of its expected cash flows, reduced for volatilityWhy not: Ignores the time value of money, which the discount rate captures.
  4. its expected cash flows discounted at a rate set by its own total volatility, whatever its correlation with other assetsWhy not: Confuses total risk with systematic risk; the rate depends on exposure to priced factors, not standalone volatility.

Price equals expected cash flows discounted at rf plus a risk premium. Price changes come from changes in expected cash flows, the risk-free rate or the premium. Standalone volatility is not the rate-setter.

A harder one

Stock X and stock Y have the same volatility. X tends to rise in recessions, while Y falls sharply in recessions, when investors' marginal utility of wealth is highest. According to the rational theory of risk premiums, which statement is most reasonable?

  1. X should have the higher expected return, because its recession payoffs are the most valuable to investors who hold itWhy not: Reverses the logic: payoffs in bad times are valuable, so X is in demand and its expected return is lower.
  2. The two should have equal expected returns, because their volatilities are equalWhy not: Treats total volatility as the measure of rewarded risk instead of covariance with bad times.
  3. Y should have the higher expected return, because it loses value when wealth is most valuable - correct
  4. Neither should earn a premium, because stock-specific risk can be diversifiedWhy not: Recession exposure is a systematic factor risk, not a diversifiable stock-specific risk.

A premium rewards covariance with bad times. Y behaves like negative insurance and must offer a higher expected return; X pays off in bad times, so investors accept less.

The hardest tier

A stock's next annual cash flow is USD 4 per share and is expected to grow at 2% a year forever. The risk-free rate is 3% and the required risk premium is 4%. If the risk premium rises to 5% with everything else unchanged, the price changes by closest to:

  1. -20.0%Why not: Reports the 20% rise in the denominator (r - g from 5% to 6%) as the price fall, forgetting that price is its reciprocal.
  2. -16.7% - correct
  3. -12.5%Why not: Ignores growth and treats price as proportional to 1/r: 7% / 8% - 1.
  4. -14.3%Why not: Takes the 1 point rise as a share of the old discount rate (1 / 7) instead of repricing the growing perpetuity.

P = CF / (r - g). Before: 4 / (0.07 - 0.02) = 80. After: 4 / (0.08 - 0.02) = 66.67, a change of -16.7%. A small rise in the premium moves price a lot because the denominator r - g is small.

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