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Lay out how value investing is carried out and account for why a value premium might exist.

FRM® Part II · Risk Management and Investment Management · Factors · FRM2.IM.2.a

The idea

Value investing buys assets that look cheap relative to a fundamental anchor and sells those that look expensive. Cheapness is measured with ratios such as book-to-market, earnings-to-price, cash-flow-to-price or dividend yield. Stocks are ranked on the ratio, the cheapest group is bought and the most expensive group sold. The Fama-French HML factor does this with four portfolios sorted by size and by book-to-market, so it averages the monthly returns of small value and big value portfolios and subtracts the average of small growth and big growth: HML = (small value + big value) ÷ 2 − (small growth + big growth) ÷ 2. Two explanations exist for the premium. The risk-based view says value firms hold assets that are costly to scale back and suffer most in bad economic times, so investors demand extra return. The behavioural view says investors extrapolate past growth and overpay for glamour stocks, and limits to arbitrage keep the mispricing alive. The usual mistake is to treat a low ratio as proof of a bargain, since some cheap stocks are value traps. Risk-based premia should persist. Mispricing premia should shrink as capital arbitrages them away.

Formulas

Fama-French HML factor return

HML = (SV + BV) ÷ 2 − (SG + BG) ÷ 2

SV
the small value portfolio return
BV
the big value portfolio return
SG
the small growth portfolio return
BG
the big growth portfolio return

Averaging across both size groups keeps the factor neutral to size; the neutral book-to-market portfolios are left out.

A practice question

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

Which of the following is a risk-based (rational) explanation for the value premium?

  1. Investors extrapolate recent strong growth in earnings and overpay for glamour stocks, leaving growth stocks overpriced.Why not: This is the behavioural (mispricing) story, not compensation for risk.
  2. Short-sale constraints and limited arbitrage capital stop investors from fully eliminating the mispricing in cheap stocks.Why not: This is a limits-to-arbitrage argument that sustains mispricing; it is not compensation for bearing risk.
  3. Value stocks have higher book values in absolute terms, which mechanically produces higher future returns.Why not: Treats the accounting ratio as the source of return; the level of book value is neither a risk nor a behavioural bias.
  4. Value firms hold assets that are costly to scale down and are hit hardest in bad times, so they must offer a higher expected return. - correct

A risk-based explanation says the premium compensates investors for bearing risk: value firms are exposed to bad times (for instance, they cannot easily shrink capital in a downturn). Extrapolation and limits to arbitrage are behavioural or institutional explanations.

A harder one

A manager forms a value portfolio from six stocks, ranked on book-to-market (book value per share divided by price). Equal weights, long the two highest book-to-market stocks and short the two lowest. Data (price, book value per share, next-period return): A (50, 40, 4%); B (20, 5, 3%); C (30, 36, 8%); D (80, 32, 1%); E (40, 40, 5%); F (60, 30, 2%). The long-short return is closest to:

  1. 4.5% - correct
  2. -4.5%Why not: Sign error or ranking on price-to-book backwards, so the expensive stocks are bought and the cheap ones sold.
  3. 4.0%Why not: Shorts all four remaining stocks instead of only the two lowest book-to-market stocks.
  4. 9.0%Why not: Adds the returns of the legs instead of averaging them (13% minus 4%).

Book-to-market: A 0.80, B 0.25, C 1.20, D 0.40, E 1.00, F 0.50. Long C and E: average 6.5%. Short B and D (lowest): average 2.0%. Long-short = 6.5% - 2.0% = 4.5%.

The hardest tier

In the Fama-French construction, stocks are sorted into small and big and into value, neutral and growth by book-to-market, giving four portfolios on either side of the neutral group. Monthly returns are: small value 3.0%, big value 1.8%, small growth 0.6%, big growth 1.0%. The monthly HML factor return is closest to:

  1. 2.4%Why not: Uses only the small-cap portfolios (small value minus small growth), ignoring big stocks, so the size effect contaminates HML.
  2. 3.2%Why not: Sums the value portfolios and subtracts the sum of the growth portfolios instead of averaging.
  3. 0.4%Why not: Averages small portfolios minus big portfolios, which is the SMB construction, not HML.
  4. 1.6% - correct

HML = average(small value, big value) - average(small growth, big growth) = (3.0 + 1.8)/2 - (0.6 + 1.0)/2 = 2.4 - 0.8 = 1.6%. Averaging across both size groups keeps HML neutral to size.

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