Beta

A stock has a beta of 1.5. If the market rises 10%, the stock is expected to rise about:

1. A.1.5%This reports beta itself as if it were the expected percentage move. Beta has no units of its own; it is the factor that scales the market's move, so it must be applied to the 10%.
2. B.10%10% is the market's own move, which is what you would expect from a stock with a beta of exactly 1.0. A beta of 1.5 says this stock tends to move half again as much, so its expected change has to exceed the market's.
3. C.6.7%6.7% divides the market move by beta instead of multiplying. Dividing also points the wrong way: a beta above 1.0 indicates amplified movement, so the expected change must be larger than 10%, not smaller.
4. D.15%Correct - 1.5 x 10%.

Why: Expected move = beta x market move = 1.5 x 10% = 15%.

The overall market portfolio has a beta of:

1. A.0Beta of zero describes an asset with no correlation to market movements, such as a risk-free Treasury bill. The market cannot have zero sensitivity to itself.
2. B.1.0Correct - the market's beta is 1.0.
3. C.UndefinedBeta is undefined only when there is no return variance to regress against, which is not the case here. The market is the benchmark the measure is built on, so its beta is the most precisely defined of all: exactly 1.0.
4. D.2.0A beta of 2.0 belongs to an aggressive individual stock expected to move twice as much as the market. Since beta measures movement relative to the market, the market cannot be twice as volatile as itself.

Why: By definition, the market has a beta of 1.0; a stock with beta above 1 is more volatile than the market.

Under CAPM, a stock's required return rises as its:

1. A.Book value risesBook value is an accounting measure of net assets and appears in valuation ratios, not in the CAPM equation. CAPM contains only the risk-free rate, beta, and the market risk premium.
2. B.Trading volume dropsFalling volume suggests thinner liquidity, and investors do demand compensation for illiquidity in the real world, so this has surface appeal. CAPM does not price liquidity at all; systematic risk measured by beta is its single risk input.
3. C.Dividend yield fallsThis confuses required return with the dividend yield component of realized return. CAPM sets the return investors demand for bearing systematic risk, regardless of whether that return arrives as dividends or appreciation.
4. D.Beta increasesCorrect - required return scales with beta.

Why: Higher beta means more systematic risk, so CAPM requires a higher expected return.

A stock with a beta of 0.8, when the market falls 10%, is expected to fall about:

1. A.8%Correct - 0.8 x 10%.
2. B.10%This ignores beta entirely and just repeats the market's own move. A beta of 0.8 means the stock is less sensitive than the market, so its expected decline must be smaller than 10%.
3. C.0.8%This treats beta as if it were a percentage return rather than a multiplier. Beta is a dimensionless sensitivity factor: multiply it by the market move of -10% to get -8%.
4. D.12.5%This divides the market move by beta (10/0.8) instead of multiplying. Dividing by a beta below 1 magnifies the move, which contradicts the fact that a 0.8-beta stock is the more defensive holding.

Why: Expected move = beta x market move = 0.8 x -10% = -8%.