Workshop & problem set questions Flashcards
Discuss the 2-pass approach to testing CAPM. Do empirical studies based on this support or reject CAPM?
[2018]
*Excess stock returns & beta have a LINEAR +VE RELATIONSHIP, consistent with CAPM
[PS2]
First pass
1. Estimate BETAS for all stock i
- r_it - r_ft = (alpha i)hat + (beta i)hat*(r_mt - r_ft) + epsilon_it
2. Compute AVERAGE (r_it - r_ft), ie. the average excess return
eg. 1000 stocks in sample -> 1000 estimates of beta and 1000 average (r_it - r_ft)
[draw graph]
Second pass
3. average (r_it - r_ft) = gamma_0 + gamma_1*(beta_i)hat + epsilon_i
[draw graph]
If CAPM holds,
- gamma_0 = 0
- gamma_1 = market risk premium
CAPM is rejected on both counts (from empirical studies) b/c
- gamma_0 is NON-ZERO
- gamma_1 is SMALLER than MARKET RISK PREMIUM
Describe the three-factor model of Fama and French.
[2018]
Fama and French 3-factor pricing equation is…
E[r_i - rf] = biE[rm - rf] + siE[R_SMB] + hi*E[R_HML]
Factors
1. rm - rf is the market return minus the risk-free rate
2. SMB is the small minus big portfolio
- the return on small-cap stocks (bottom 50%) minus the return on large-cap stocks (top 50%)
3. HML is the high minus low portfolio
- the return on high book-to-market stocks (top 30%) minus the return on low book-to-market stocks (bottom 30%)
4. All three are zero investment portfolios
How are the factors of the Fama and French three-factor model constructed?
[2018]
- Sort all firms into 2 SIZE groups (S and B) and 3 B/M groups (L,M,H)
- Form 6 value-weighted portfolios
- HML = (HS + HB / 2) - (LS + LB / 2)
and SMB = (HS + MS + LS / 3) - (HB + MB + LB / 3)
Advantages & disadvantages of the Fama and French three-factor model relative to the CAPM
[2018, 2016]
+ The factors are empirically motivated and do not come from theory
+ works better than CAPM
- These factors might also be capturing some unknown risk factors
- no clear theoretical motivation
CAPM question
1. What is the economic interpretation of the intercept?
2. How can we be sure that the evidence is inconsistent with the CAPM?
[2016]
- The intercept (ALPHA) captures the PRICING ERROR of the CAPM
- We need to test if the intercepts are JOINTLY different from zero
2 advantages of the Fama-MacBeth approach of testing the CAPM relative to the one-pass approach
[2016]
- Can estimate RISK PREMIUM associated w/ the factor
- Allows for TIME-VARYING number of firms
Describe the Fama-MacBeth approach of testing the CAPM.
[2016]
Fama-MacBeth estimate monthly CROSS-SECTIONAL REGRESSIONS of returns vs BETAS for portfolios sorted by beta values estimated from a prior period,
then AVERAGE the estimates of the risk premium (slope) and the risk-free rate (intercept)
- Definition of an Arbitrage opportunity
- Main assumptions of Ross’ (1976) Arbitrage Pricing Theory
[2017]
- An arbitrage opportunity arises when an investor can make sure profits WITHOUT making a NET INVESTMENT
eg. an investment strategy that has a +ve cash flow TODAY and zero cash flows in the FUTURE in all states of nature - APT
- No arbitrage opportunities
- Returns can be described by FACTORS
- Idiosyncratic risk is DIVERSIFIED AWAY {so only systematic factors matter}
Describe how to construct an event study
- Pick an ASSET PRICING MODEL, eg. CAPM
- Estimate BETA in the pre-event window, eg. 3 months
- Calculate ABNORMAL RETURNS in the event window, eg. 3 days around the event
- Calculate ABNORMAL RETURNS in the post-event window, eg. following 3 months
[draw timeline]
- Plot CAR
If market is EFFICIENT and the event study is around a stock-split announcement,
- expect +ve AR in the event window and…
- …zero CAR in the post-event window
Rolls’s (1977) critique
In particular, under what circumstances would i) we incorrectly reject the CAPM, and ii) incorrectly accept the CAPM?
[2015]
- Test of CAPM that does not use the TRUE MARKET PORTFOLIO is not a true test of CAPM
- It is only a test of whether the chosen index is ex-post efficient - Choose ex-post INEFFICIENT portfolio
=> can WRONGLY REJECT CAPM - Choose ex-post EFFICIENT portfolio
=> can WRONGLY ACCEPT CAPM (true market portfolio may be inefficient)
Given that the expected lawsuit settlement amount is $2m and the realised amount is $5m (hence surprise of $3m),
Carefully explain your reasoning in the framework in the market efficiency tests based on EVENT STUDIES.
[PS10]
- Considering the abnormal return of 3%, clearly investors were POSITIVELY SURPRISED and the settlement was perceived as good news.
- In the context of the event study literature, the CAR of PG would plot as a FLAT LINE with a discrete POSITIVE JUMP on announcement day (not necessarily on the
day of the settlement). - If markets are EFFICIENT in incorporating the news, the plot
would show a FLAT LINE after announcement day. - If INSIDERS that knew the amount
of the settlement BEFORE the public announcement day TRADED the stock, the plot could show an UPWARD DRIFT before the announcement.
What would happen to market efficiency if all investors attempted to follow a passive strategy?
[PS5]
- If everyone follows a passive strategy, sooner or later prices will fail to reflect new information.
- At this point there are PROFIT OPPORTUNITIES for active investors who uncover mispriced securities.
- As they buy and sell these assets, prices again will be driven to fair levels.
Formula for the Return on Canadian bond
[PS10]
Return = coupon income + forward premium/discount (relative to the spot exchange rate) + %price change (ie. capital gain/loss on the bond)
International CAPM: what is the “relationship” between Currency exposures of stocks with Expected return?
- NEGATIVE currency exposures of a stock result in a LOWER EXPECTED RETURN
- POSITIVE currency exposures result in a HIGHER EXPECTED RETURN
- Is there evidence of an interaction between momentum and value strategies?
- Can higher profits be obtained by taking both past returns and B/M into account?
[PS10]
Momentum profits are LARGE and SIGNIFICANT (b/c t-stat > 2) after controlling for B/M
- holding B/M constant, ranking stocks on past performance and forming winner-loser hedge portfolios yields ABNORMAL RETURNS (provided that these portfolios have the same exposure to risk factors)
- therefore, the table shows that momentum strategies are profitable.
Value strategies profits are large and significant after controlling for past returns
- holding past returns constant, strategies that buy high B/M stocks and sell low B/M stocks yield ABNORMAL RETURNS (provided that these portfolios have the same exposure to risk factors)
- therefore, the table shows that value strategies are profitable
There is EVIDENCE of an INTERACTION between past returns and B/M:
- Momentum profits decrease with B/M
- Profits from value strategies show some tendency to decrease with past performance
- Yes. We can make higher profits by implementing momentum or value strategies only on a SUBSET of stocks
eg. implement a MOMENTUM strategy only on the LOW B/M stocks. The profits would be 1.47% per month
eg. perform a VALUE strategy only on the stocks that exhibit relatively poor past performance (LOSERS)
