FI 478

What is not a risk/cost for ADR arbitrage

basis risk In ADR arbitrage (e.g., Alibaba shares in the US vs. HK), news will impact identically long and short legs, hence no basis risk. But investors in one of the markets (e.g., US) can push the price creating a spread between US and domestic prices, hence noise trader risk. Of course, costs such bid-ask spread or stock borrowing fees always affect arbitrage profitability.

What is NOT an example of arbitrage in practice that we studied

bond arbitrage

In the merge arbitrage (assuming a cash deal) strategy, you ...

buy stock of the target We buy stock of the company that is being purchased and hope that the deal is completed (cash deal - so no need to hedge by selling the acquirer )

What is the main risk with pair trading (e.g., Ford vs. GM)?

idiosyncratic news risk (basis risk) Because Ford and GM are in the same industry, macro and industry news will affect them similarly. The main risk is that some news (e.g. car recalls or supplier disruptions) can affect one stock but not the other.

What is the trading idea behind the post-earnings announcement drift anomaly?

stock prices increase after positive earnings surprises

According to Mark Cuban, the drawback of diversification is ...

that it is hard to find many mispriced stocks to build a diversified portfolio

What is NOT the reason why the data extracted from satellite image used to predict return, but does not anymore?

the data can better predict earnings due to advances in AI It is difficult to beat the market with the data that are cheap, easy-to-use, and hence everyone is using it. These factors overweigh the fact that advances in AI let you extract better signals about future earnings from the data.

Law of One Price means that ...

two assets with the same payoffs must have the same price See slide 6

What is the idea behind the hard-to-borrow anomaly? Stocks that are hard-to-short ... before transaction costs.

underperform

ABC's expected return is 10%, while CAPM estimate its returns at 9% given ABC's beta. ABC is ...

underpriced

The actual return of the asset is 10%, but based on its beta CAPM estimates its required return as 8%. The asset is ...

underpriced "underpriced" = "cheap" = "good buy," this asset has higher return (10%) than assets with similar beta that are fairly priced (8%), we get more return for less risk.

What is NOT part of the "textbook" definition of arbitrage

you can occasionally lose money, but you make money most of the time

In a one factor model, the risk premium is 6%, and the risk free rate is 2%. Portfolios A and B have betas of 1 and 1.5 and expected returns of 8% and 12%. What is B's alpha?

1% Alpha = Actual Exp Return - Exp Return from APT = 12% - (2% + 1.5*6%) =1%

Suppose you invest in a stock for four months. The expected return for the investment is 15%, and the expected volatility is 8%. What is the annualized Sharpe ratio? Assume that the annual risk-free rate is 1%. Pick the closest number.

1) Annualized return = (1+15%)^3-1=52% 2) Annualized volatility = 8%*sqrt(3) = 13.85% 3) Sharpe ratio = (R -rf)/s = (52%-1%)/13.85%=3.68

Three months ago you had $1000 in your account. Since then, your account had the following returns in the last three months: -20%, 30%, 10%. What is annualized HPR for your account?

1. Compute HPR=(1-0.2)(1+0.3)(1+0.1)-1=14.4% 2. Annualized HPR=(1+0.144)^4-1=71.3%, because 4 3-month periods in a year

Answer the following questions using regression results for XLF (Financial stock ETF). What is XLF's beta? If can't see the image, the link https://www.dropbox.com/s/xcrog08280em212/CAPM_XLF.png

1.1

GM stock currently trades at $10. Consider the following probability space with the corresponding price for GM stock: Scenario: Probability: GM price: Good: 0.5 $11 Bad: 0.5 $9 What's the expected volatility for GM stock?

10%

The current price of TSLA is $900. It can go up to $950 with a probability of 60% or drop to $800 with a probability of 40%. Compute the expected volatility. Pick the closest number.

10%

In a two factor model, the two risk premiums are lambda1=5% and lambda2=10%. Portfolio XYZ has factor betas of beta1=0.5 and beta2=0.7. Risk free rate is 2%. What's expected return for XYZ according to this model?

12% =2%+0.5*5%+0.7*10%=11.50%

You bought a share of PFE (Pfizer Inc) for $50 two month ago. You sold the PFE stock today for $75. Meanwhile, the stock paid $2 in dividends/share. Compute the annualized HPR (Holding period return). Pick the closet number.

1230%=((75+2)/50)^6-1=1233.9%, 6 two-month periods in a year

Your returns in the previous three months are -10%, 15%, 10%. What is you HPR over the entire period?

14%

You build an equally weighted portfolio of 300 stocks with the average correlation of 10% and average variance of 0.2. What is the approximate volatility of this portfolio?

15%

Your investment has annualized return of 20%, volatility of 10%. What is the Sharpe ratio of your strategy? Assume that the risk-free rate is 1%. Pick the closest number.

2

In the ADR arbitrage, you sell one share of an ADR for $10 and buy local shares of the same company for $8. You close the position then the prices converge at $12. What are your $ profits?

2 You make $4 (=12-8) from the long position and lose $2 on the short ADR leg. Thus, your profit is $2 (=4-2)

If the market is up 2% today, what is your best guess for how much XLF's price will increase? If can't see the image, the link https://www.dropbox.com/s/xcrog08280em212/CAPM_XLF.png

2.2% Ret = rf + b*(Ret(Market)-rf)+eps, eps is zero on average and rf can be ignored for large market swings. Thus, Ret ~ b*Ret(M) = 1.1*2=2.2%

Suppose the three-month volatility (σ) that Ford's stock is 10%. What is the annualized volatility?

20%

You bought a stock for $20 and sold six months later for $23. The the stock paid a dividend worth $1 during your holding period. What's your holding period return (over six months). Prick the closest number.

20%

Typical correlation between two random US stocks is closest to ...

30%

Which method is NOT used to improve volatility estimates/forecasts in practice?

Adjust volatility proportional to expected return

What is NOT one of CAPM assumptions?

All investors have the same risk aversion

Your HPR over two years is 50%. Annualized HPR is...

Annualize HPR=(1+50%)^0.5-1=22.47%

You hold a stock for one day and made 1% return. What's your annualized return?

Annualized HPR=(1+1%)^252-1=1127%; Compounding really matters here. 252 trading days in a year.

Which statement about diversification (with positively correlated assets) is correct?

As the number of assets increase, total risk typically falls but a decreasing rate.

Compute covariance for the following example: Three scenarios (1,2,3) with probabilities (20%, 30%, and 50%). Two stocks: Apple and GM. Apple's and GM's returns for the three scenarios are (5%,-5%,0%) and (3%,-4%,2%).

Expected returns are zero for both stocks. (Ret_i(AAPL)-ExpRet(AAPL))*(Ret_i(GM)-ExpRet(GM)) for three scenarios are 0.0013, 0.0022, 0.0000 Covariance = 0.2*0.0013+0.3*0.0022+0.5*0.0000=0.000917

In theory, should CAPM work for computing expected return for Bitcoin?

CAPM can price any asset in theory

Which TWO points David Swensen made in the video about his approach to endowment management?

Endowments have long-term orientation and should take more equity risk Endowments should diversify across asset classes

In CAPM, assets with higher volatility always have higher expected return ("higher return for higher risk")

In CAPM the risk is measured by beta not volatility. An asset can have high volatility, but if it is negatively correlated with the market, then its expected return will be low.

what is NOT on the list of CAPM assumptions?

Investor have the same risk tolerance

Which of this assumptions is required by CAPM?

Investors pay no transaction costs

Why diversification is called "the only free lunch"?

It helps reduce idiosyncratic risk by increasing number of assets

You invest in an equally-weighted portfolio of 1,000 stocks with an average correlation of 30%. Average volatility is 40%. What is portfolio variance?

Slides 7-8. Portfolio variance = correlation * volatility^2 = 30% * 40%^2 = 0.048

What is NOT true about market volatility?

Slowly increases during the crises

You invested $100 of your money and another $100 borrowed from a friend into an XYZ stock. Its price increased from $10 when you bought to $11 when you closed the position and returned money to your friend (assume zero interest). What your return (on the capital)? Pick the closest number

Stock's return is 10%, you made (100+100)*1.1 -100-100=$20 You invested $100 of your capital, you made $20 - your return 20%=20/100 Thus, you can increase your return by using leverage (borrowed money)

The Fama-French model includes three factors: ER_P - rf=β_M (ER_M-r_f )+β_SMB (S-B)+β_HML (H-L) If we apply this model to the market portfolio, then betas for (M,SMB,HML) are

(1,0,0) See slide 33 and the corresponding video. In short, return of a market portfolio is perfectly predicted by market portfolio (yes, same thing on left and right), hence market beta is 1, the other betas are zero because SMB and HML can't add to an already perfect forecast.

Suppose the risk premium on the single factor in 8%, and the risk-free rate is 2%. There are three well-diversified portfolios with the following characteristics: A BetaA = 0.8 ExpRetA=8.4% B BetaB = 1 ExpRetB=10.5% C BetaC = 1.2 ExpRetC=11.6% Which of these is an arbitrage portfolio? E.g., A+B-0.5C means buy $1 of A, $1 of B, and sell $0.5 of C Hint: see slide 21

-0.5A+B-0.5C We can check that A and C are fairly price (zero alpha), while B has a positive alpha (10.5%-(2%+1*8%)=0.5%). Thus, we want to buy B and hedge the risk with A and C. A portfolio with 50/50 between A and C has a beta of 0.5*0.8+0.5*1.2=1, the same as B. Overall, we buy B and sell hedge portfolio (0.5A+0.5C)-> -0.5A+B-0.5C is an arbitrage portfolio. Let's double-check the answer. An arbitrage portfolio must have three properties. 1. Self-financed (no initial investment). Indeed, (-0.5A+B-0.5C) -> -0.5+1-0.5=0, get $0.5+$0.5 from shorting A and C and buying B with this $1 2.No risk. We assume that A,B,C are well-diversified, so no idiosyncratic risk. And no systematic risk, because the beta is zero beta(-0.5A+B-0.5C) = -0.5*0.8+1*1-0.5*1.2=0 3. Positive return. Exp Ret (-0.5A+B-0.5C) = -0.5*8.4% +1*10.5% -0.5*11.6% = 0.5%>0

ABC has expected return and volatility of 10% and 30%. Market portfolio has expected return and volatility of 8% and 15%. ABC's beta is 1.5. Risk free rate 2%. Compute ABC's alpha.

-1%

What is the beta of a portfolio that invests 20% in the risk free asset and 80% in the market portfolio?

0.8

A typical US stock has a beta of ...

1

XLF's returns change with the market and due to idiosyncratic news. The share of XLF's return variation which is due to idiosyncratic news is... If can't see the image, the link https://www.dropbox.com/s/xcrog08280em212/CAPM_XLF.png

35% R2 show how much of XLF's return variation is driven by the market return, the reminder is due to idiosyncratic news. 34.3% = 100%-65.7%

Your three-month HPR is 8%. What is your annualized return?

36%

Stock ABC has a 30% volatility and a 30% correlation with the market portfolio. Risk free rate is 1%, expected return and volatility on the market are 6% and 15%. According to CAPM, ABC's expected return is...

4%

The average annual volatility of S&P 500 index is approximately 20% last. Find the average annual variance of S&P 500. Pick the closest number.

4%

You have lost 30% on $IBM the day before yesterday. But fortunately, it went up 70% yesterday, and 20% today. What is your total return over these three days? Pick the closest number.

40%=(1-30%)*(1+70%)*(1+20%)-1

Suppose that the daily volatility (σ) of Apple's stock is 3%. Find the annualized volatility of the stock. Pick the closest number. Pick the closest number.

48%=SQRT(252)*3=47.62%

What is expected return on XYZ if its beta is 0.6? E(RM) = 8%, rf=2%

5.5% ER=rf+beta*(ERM-rf)=2%+0.6*(8%-2%)=5.6%

Current price of IBM is $50. In four months, the price of the stock is expected to be at $75 with probability of 60%, or at $30 with probability of 40%. What is the annualized expected return? Pick the closest number.

50%

You have $2,000 to invest. If you invest your $2,000 in micro-cap stocks, the total value of your investment after one year will become $4,500 with probability of 50%, $2,500 with probability of 25%, and $1,000 with probability of 25%. Find the expected return of your investment for the year. Pick the closest number.

60%

Suppose the volatility (σ) of Ford's stock was 2% for the past one month. Find the annualized volatility of Ford's stock. Pick the closest number.

7%=2%*SQRT(12)=6.93%

Compute expected return required by CAPM for XYZ if β_XYZ = -0.5, rf=1%, E(R_M)=5%, ρ_(XYZ,M)=-0.7.

=1%-0.5*(0.05-0.01)=-1%

Suppose the volatility (σ) of McDonald's stock was 2% for the past three months. Find the annualized volatility of McDonald's stock. Pick the closest number.

=2%*sqrt(4)=4%, 4 three-month periods in a year

What is NOT a common way to estimate probabilities?

Based on the Sharpe ratio

Consider the following example: E(rM) = 6%, σ(M) = 15%, rf = 2% E(rA) = 10%, σ(A) = 30%, ρ_(A,M) = 0.8 What's return required by CAPM?

Beta = 0.8*0.3/0.15=1.6 Expected return = 2%+1.6*(6%-2%)=8.4%

You construct an equally weighted portfolio of A, B, and C, which have betas of 0.5, 0.8, and 1.1. Portfolio beta is ...

Beta = 1/3*0.5 + 1/3*0.8 + 1/3*1.1 = 0.8

If asset's return is uncorrelated with the market, then asset's expected return is

Beta = Corr * Volatility A/ Volatility M = 0 as Corr=0 E(r_A)=rf+beta*(E(rM)-rf)=rf+0*(E(rM)-rf)=rf

Compute correlation for the previous example: Three scenarios (1,2,3) with probabilities (20%, 30%, and 50%). Two stocks: Apple and GM. Apple's and GM's returns for the three scenarios are (5%,-5%,0%) and (3%,-4%,2%).

Expected returns are zero for both stocks. (Ret_i(AAPL)-ExpRet(AAPL))^2 for three scenarios are 0.0025, 0.0025, 0; For GM: 0.0007, 0.00188, 0.000278. Variances for AAPL and GM are 0.00125 0.00084. Volatilities are sqrt(variance): 0.035355339 0.029059326. Correlation = Covariance/{Volatility(AAPL)*Volatility(GM)}=0.000916667/(0.035355339*0.029059326)=0.892

What fraction return variation for this stock is explain by its idiosyncratic (non-market-wide) news?

Explained my Idiosyncratic News =100% - R^2

Which model works better at explaining average portfolio returns, CAPM or Fama-French?

Fama-French See slides 28-29

You sold a stock short at $50 betting that it will decrease. But the price rockets to $100 due to a short squeeze, and you have to cover your short at this price. What is your holding period return?

HPR for the short size will be the reverse of the HPR for the long side. Thus, HPR=-(100/50-1)=-100%

You bought a stock at $5 and sold it at $6. Meanwhile the stock paid a dividend of 10 cents. What's your holding period return. Prick the closest number.

HPR=(6+0.1)/5-1=22%

Compute CAPM beta for XYZ. If you know volatility for XYZ and the market: 𝜎_𝑋𝑌𝑍=30%, 𝜎_𝑀=20%, and correlation 𝜌_(𝑋𝑌𝑍,𝑀)=0.4. Pick the closest number.

Hide Feedback =0.3*0.4/0.2=0.6

You observe monthly historical returns of 6%, -1%, -4%, 5%, 0%. Your estimate of the expected future return (based on these historical data) is ...

Hide Feedback =AVERAGE(6%, -1%, -4%, 5%, 0%) See slide 25

We use S&P500 as a proxy for the market portfolio, but in theory it should include ...

Market portfolio should include all risky assets: stocks, commodities, real-estate, and more. Watch "Market portfolio" video

Answer the following questions using regression results for XLF (Financial stock ETF). Is the alpha significantly negative? If can't see the image, the link https://www.dropbox.com/s/xcrog08280em212/CAPM_XLF.png

Negative, but insignificant The 95% confidence interval for alpha is -072% to 0.17% and thus includes zero. The estimate for alpha is negative but not significantly different from zero.

You build an equally weighted portfolio of 20 assets that are uncorrelated. Their average volatility is 0.2. What is the approximate volatility of this portfolio?

See slide 4. Note that variance = volatility^2 Portfolio volatility = sqrt(Average asset variance/N assets) = Average volatility/sqrt(N)=0.2/sqrt(20)=0.0447 It is zero only in the limit as N goes to infinity.

You build an equally weighted portfolio of 10 assets that are uncorrelated. Their average variance is 0.16. What is the approximate variance of this portfolio?

See slide 4. Portfolio variance = 0.16/10 = 0.012 = Average asset variance/N assets

You invest $200 in stock A and $400 in B. A has a beta of 0.5 and B's beta is 2. What is the beta of the combined portfolio?

Portfolio weights for A and B are: 33%=200/(200+400), 66%=1-0.33 Portfolio beta = 33%*0.5+66%*2=1.485

Pick two main assumptions of arbitrage pricing theory (APT)

Prices are set so that they do not allow arbitrage All returns are driven by several common factors Unlike CAPM that requires that all investors do the same thing (e.g. minimize volatility and agree on expected returns), APT primarily requires only no arbitrage and assumes factor structure for returns (hence the name). The model works even with thousands of unsophisticated investors, if arbitragers are doing their job.

Which statement is TRUE about expected return?

Return depends on the leverage 1. Return does not depend on how much money is put in as $X*10%/$X=10% 2. We can easily annualize return using (1+Ret)^t-1 formula 3.Correct: If you double your leverage, your return will also double. 3. (Xend+Div)/Xbeg-1 -> so dividends accrue at the end; if they accrued at the beginning we would have to add their future value.

Which of the stock pair has the lowest correlation?

Saudi Arabian Oil Co., InnoCare Pharma Ltd (HK) Most dissimilar industry and geography

You invest in an equally weighted portfolio of 100,000 uncorrelated assets. What is portfolio's return variance?

This is a very large number of asset that drives variance close to zero. E.g. assume that average variance is 1^2=1 (very high, like Bitcoin crazy vol), yet portfolio variance =1/100,000 ~ 0

Which statement is TRUE about expected return and volatility?

Volatility increases during crises

Rarely but volatility can be negative

Volatility is ~ squared distances, and distance is always non-negative

CAPM can be viewed as a single factor APT

Yes

You bought 2 ounces of gold at $2,000 per ounce. You sold it six months later for $2100/ounce. You stored gold in a warehouse and paid the total storage costs of $50. What is your holding period return (no need to annualize)? Pick the closest number.

Your costs per ounce are $50/2=$25. Thus HPR = (2100-25)/2000-1=3.75%

After anomalies are discovered and published, their alpha ...

decrease More investors learn about the anomaly after its published, trade on it, and reduce its profitability. See slide 28

Benefits of international diversification (for US investors who want to add emerging equities to their portfolio) ... over time (from 1980 to 2020)

decreased Slide 12. Correlation between S&P500 and other worlds markets increased to ~0.95 in mid 90s reducing the benefits of diversification

What is NOT a form of market efficiency?

fundamental analsysis

The Fama-French model includes three factors: ER_P - rf=β_M (ER_M-r_f )+β_SMB (S-B)+β_HML (H-L) Betas for a mutual fund MF are (M,SMB,HML)=(1,-0.5,0.5). What can you tell about fund's strategy? This is a ... fund

large value

Which factor is not part of the Fama-French model

liquidity slides 25-26

What is the main risk for ADR arbitrage?

noise trader risk

Arbitrage opportunities are larger ...

period of market stress, crisis See slide 15 and the videos

If beta is positive the sign of the correlation between the asset and the market is...

positive β_A=(ρ_(A,M) σ_A)/σ_M -> volatilities are non-negative, so correlation determines the sign for beta

To compute correlation between to stocks we use ...

returns

We test how past returns predict future returns r_(i,t)=α+γ r_(i,t-1)+ε_(i,t) If the past return is over one month we observe ... if it is over past six months, we observe ...

reversal, momentum Short-term reversal (up to one month) - prices recover after a bad month; mid-term momentum (up to 12 months) - prices continue falling after a bad six-month returns.

According to the joint hypothesis problem, if your strategy has an alpha relative to FF3 model, it must be due to ... Hint: analogy with buying a house. If you see a house that is cheap relative to Zillow quant model, it could be due to ...

risk or mispricing, but we can't tell which Joint hypothesis problem, as the name suggests, tells us that it is really difficult to distinguish between mispricing (true alpha) and omitted risk factor (beta). For example, momentum has an alpha relative to FF3, but occasionally has crashes. Is momentum due to risk or mispricing? We do not know.

You think that XYZ will report earnings per share of 10 cents, while analysts expect an EPS of 12 cents per share. If you are confident in your forecast, you should ...

sell If EPS is 10 cents, it would be a negative surprise for the market, and the price will drop, you need to sell

We predict future returns with signal s 𝑟_(𝑖,𝑡)=𝛼+𝛾*s(𝑖,𝑡−1)+𝜀_(𝑖,𝑡) and find that gamma is negative (𝛾 <0) and significant If s is positive (higher than normal), we should ... Hint: consider an example, short interest is a negative signal (𝛾 <0 ) because short seller, who bet that the stock price will drop, are often right. If short interest is particularly high (S higher than average), we should ...

sell Positive signal times negative 𝛾 predict negative return, so we should sell

Three portfolios (A, B, and C) have the following parameters relative to a one-factor APT. Portfolio, Beta, Alpha A, 0.5, 0% B, 1, 2% C, 1.2, 0% How do you construct an arbitrage portfolio to exploit relative mispricing between portfolios A, B, and C?

sell A, buy B, sell C

Which form of market efficiency are we testing if we sort stocks based on market-to-book accounting ratio?

semi-strong B/M is accounting *public* info that is beyond just prices and volume (required for weak form), thus we move to the next form - semi-strong

The Fama-French model includes three factors: ER_P - rf=β_M (ER_M-r_f )+β_SMB (S-B)+β_HML (H-L) Betas for a mutual fund MF are (M,SMB,HML)=(1,1,1). What can you tell about fund's strategy? This is a ... fund

small value See videos. This fund has a positive exposure to size (Bsmb=1) and value (Bhml=1), thus it overweighs small value stocks in its portfolio. SMB = Small - Big; HML = Value - Growth (high-Low).