Finance

Question 1

Explain the distribution of US equity returns

Answer 1

1) Leptokurtic (fat tails). Compared to normal distribution, likelihood of very good and very bad returns much higher. Gives rise to “black swan” events
2) Negatively skewed. Negative returns more likely.

Question 2

Show asset price formula. What is mt+1

Answer 2

The price of an asset is the future payoff discounted by SDF.

mt+1 is the stochastic discount factor.

It can also be written as mt= 1/ 1 + rf

Question 3

How can the asset price formula be expanded? What happens if the covariance term is positive/negative?

Answer 3

If cov>0, asset pays off when MU is high. This makes it a good hedge, and helps to smooth consumption. Everyone likes this, so price goes up.

If cov<0, asset pays well when MU is low. This destabilises consumption profile, demand is low, so price will fall.

Question 4

Show the CCAPM equation and outline what it is

Answer 4

CCAPM is a single factor system. The only risk factor is consumption growth. Only non-diversifable risk is priced.

Question 5

Using the standard asset pricing formula, p=E(mx), determine the price of a zero-coupon risk-free bond paying off 1 next period. What is the gross return on the bond?

Answer 5

Question 6

Would a risk-averse investor like leptokurtosis? Explain

Answer 6

A leptokurtic distribution is when there is a greater chance of getting a very bad and a very good outcome. If you are risk-averse, the pain of the bad outweighs the gain of the good.

They dislike letpokurtosis.

Question 7

Give the formula for expected excess returns

Answer 7

Question 8

What is the equity premium puzzle? How can you provide a solution to understanding it?

Answer 8

CCAPM can only explain about 1/10 of the historic premium. Consumption is stable, so there is small covariance between returns and consumption growth

Solutions:
- If perceived consumption volatility was higher, this could mitigate. People might fear rare disasters
- Habit persistence implies people become “addicted” to current consumption level
- Heterogenous agents: consumption of rich comoves with equity returns
- Incomplete markets: if people cannot insure themselves v idiosyncratic risk, they may be reluctant to take on additional risk

Question 9

How does CCAPM explain time-series variation in returns?

Answer 9

We look at conditional mean. Test random walk (see model) b should be zero.

Question 10

Give the CCAPM in beta representation

Answer 10

Beta is the coefficient of gc. It is the consumption beta, the “quantity of risk”.

You can also write theta var(gc) as lambda. Lambda is independent of the asset: the “price” of risk. It is the risk premium for bearing consumption risk

Can write this as ri-rf = alpha + beta(lambda) + error

Question 11

Explain the Fama-French model

Answer 11

Organises by size (smallest), then by value (book-to-market ratio)

Question 12

What is shorting?

Answer 12

Bet against a stock. Gain if it falls in value

Question 13

Outline a zero-cost portfolio simple example

Answer 13

There are 2 stocks, A and B. You only own A. Think A will go down, B will go up. Short A, borrow, commit to repaying at the end of the month. Sell it for 1 immediately, and purchase B. Buy A at the new low value and return, hopefully B has gone up as well.

SMB and HML are of this kind.

Question 14

Explain how zero-cost portfolios eliminate global risk

Answer 14

It uses differences in idiosyncratic risk

Question 15

Explain the stochastic discount factor (m). How would you measure it?

Answer 15

Must affect the average person. High m implies bad times.

Any asset pricing model is a model of m:
1) CAPM: m = a - bRm
2) CCAPM: m = a - bgc
3) Fama-French Three-Factor model (see model)
- VALUE: when HML low, value stocks are doing badly, usually in a recession. This is due to greater adjustment costs, human capital risk
- SIZE: when SMB low, small stocks doing relatively badly. This is when liquidity is low. People want to hold liquid assets, so the demand for small illiquid stocks is low.

Question 16

One explanation for the equity premium puzzle is the possibility of rare disasters. Would hyperinflation constitute a rare disaster?

Answer 16

For it to explain the equity premium, rare disasters would need to impact equities more than bonds. But hyperinflayion affects bonds more since they pay a fixed amount of return.

Question 17

True or false:
According to Fama-French, small stocks are underpriced as they are overlooked, so they pay higher returns.

Answer 17

False. Small stocks pay higher as they comove with SMB risk factor. Small stocks are susceptible to all risk in SMB

Question 18

True or false:
According to Fama-French, if you break up a larger firm into smaller ones, investing in them will lead to higher returns

Answer 18

False. Nothing will change about its fundamental performance. The beta on SMB should not change. You could say they they become more illiquid when split up though.

Question 19

True or false:
Value stocks tend to move together

Answer 19

True. They do move together, this is the risk. By arbitrage, we cannot have a situation where the value portfolio pays a high premium and variability across value firms “cancel out”

Question 20

Explain the factors in the Fama-French model

Answer 20

HML factor: average excess returns of value stocks over growth stocks. Long value stocks and short growth stocks. This is a risk premium
SMB factor: average excess returns of small firms over large firms. Long small stocks and short large stocks.
Betas indicate how stock comoves with the respective risk factor. This is different for each asset. The risk premia, SMB and HML are constant.

Question 21

Explain the WML risk premium. Explain the behavioural explanations for this

Answer 21

Momentum. Short the losers and long the winners. This counters efficient markets. It does not have a natural risk-based story. The biggest risk is crash risk.

Behavioural explanations:
- Overreaction
- Herding
- Underreaction. Does not really work with greater technology. This is caused by the disposition effect.

Question 22

Show the Carhart model.

Answer 22

Fama-French but with momentum. Momentum has the highest Sharpe ratio

Question 23

What happens if you find a portfolio with a robust and positive alpha?

Answer 23

• Could be a fluke
• Could be something overlooked in the marketplace
• Genuine risk
• Risk that is narrowly held
• Tastes/behavioural

Question 24

Explain the low-volatility puzzle

Answer 24

Cannot be explained by standard models.

If you go long stocks with low volatility, and short volatile stocks, it has positive excess returns. Could be explained by:
1) lottery preferences and “familiarity bias”
2) Fund managers receive bonuses based on higher returns

Question 25

What is the efficient markets hypothesis

Answer 25

You can never attain a persistent alpha since the price is always right

Question 26

One explanation for the low volatility anomaly is there is excess demand for high volatility stocks. One theory is “lottery preferences”. Does the existence of the favourite long-shot bias support this theory?

Answer 26

The favourite long-shot bias is consistent with lottery preferences. The bias suggest people wager too much on the longshots and too little on the favourites (which end up paying best)

Question 27

Explain the systematic factors affecting bonds

Answer 27

1) Maturity
2) Default
3) Liquidity

Question 28

What is TIPS? What is the yield spread/curve?

Answer 28

Treasury Inflation-Protected Securities provide a fixed real rate of return. The TIPS market is illiquid though.

The yield spread is the difference between the short and long-run rates. The yield curve shows maturity (x) and yield (y)

Question 29

What is the Fisher equation for calculating interest rate?

Answer 29

i=r+Π^e

Sum of the real rate and expected inflation (breakeven inflation)

Question 30

Show the Pure Expectations Hypothesis equation

Answer 30

Question 31

What does PEH tell us about whether to choose short-run or long-run bonds?

Answer 31

PEH says neither. The holding period returns are equal

Question 32

Explain a PEH implication of it not materialising

Answer 32

If the long-run bond has an excess return, this is a risk premium. Typically occurs during recessions, where short-run rates remain low. This is a reward for risk.

Another reason could be Market Segmentation Theory (MST) where movements in short-run bonds are independent of long-run bonds. In the extreme case, there is no arbitrage forces connecting them.

Question 33

Show how the PEH can incorporate inflation through QE

Answer 33

Inflation comes from the CB target. MP can affect long rates but only of the first few terms. CB communicates through signalling, by purchasing large quantities of bonds, and showing credible commitment

Question 34

Show the forward rate equation of PEH. What does this mean compared to the initial one?

Answer 34

f2 = Ey21. If PEH is wrong, the forward rate will also be wrong

Question 35

Show the Uncovered Interest Rate Parity (UIP) equation

Answer 35

Where e euros = 1 dollar

i is the net return for investing domestically
RHS is the interes rate return plus expected % depreciation depreciation of domestic currency

Question 36

What is Covered Interest Rate Parity (CIP)? Show the equation

Answer 36

Same as UIP but use a forward contract to eliminate uncertainty. Buy currency forward to hedge against currency risk

Question 37

What is carry trade? What is the theory? What are the risks associated?

Answer 37

Borrow in funding currency, put money in investment currency. It fails in bas times.

According to UIP, there should be no carry trade, excess returns should be zero. Depreciation of the foreign currency should offset the interest rate differential

Carry trade underperforms when world economy is bad:
- Volatility in currency markets
- Volatility in stock markets
- US economy declines

Question 38

In recessions, there is typically excess returns on holding long-run bonds. If richer people are less risk-averse, they end up liquidating assets during a recession. So in equilibrium, assets are held by more risk-averse people. What implication does this have on excess returns during recessions?

Answer 38

Equilbrium excess returns are E(ri-rf) = θcov(gc,ri). This means as θ rises, we have a higher risk premium, and the excess returns are higher

Question 39

According to pure expectations theory, how does QE affect bond prices? (QE is when CB purchases long-run bonds in an effort to reduce their yield)

Answer 39

According to PEH, with QE, if this is successful, y12 falls above. Assuming y11 and Ey12 are given, then this condition no longer holds.
Purchasing long-run bonds now pays less, so private demand will fall. The prices will fall, and the yields will rise again back to the initial value. In this sense QE does not work

Question 40

Before the 1997 Asian currency crashes, local interest rates were 20%, while dollar rates are 5%. What did the theory of uncovered interest rate parity (UIP) predict?

Answer 40

UIP is that i = i(star) + %Δe
LHS is the return to investing domestically. RHS is the return to investing abroad. We can say that we get enhanced returns from the foreign currency appreciating. An implication is that is the local interest rate is higher than the foreign interest rate, the domestic one will depreciate.
Generally, UIP predicts the high interest rate currency depreciates.

Question 41

True or false: the success of the carry trade relies on the investment/target currency appreciating against the funding currency.

Answer 41

This is false. The carry trade can still be successful if the high interest rate country’s currency depreciates. It just should not be more than the interest rate differential.

Question 42

What are the implications of using a safe haven currency for the funding currency in the carry trade?

Answer 42

Safe haven currencies tend to appreciate in value during recessions. If you are borrowing in a safe-haven currency then repaying in a recession means repaying in an expensive currency. Using such a currency to fund is risky.

Question 43

If I purchase one dollar forward today at price ft, so I can purchase a dollar next period at the predetermined rate. If the exchange rate next period is et+1 what is the payoff next period?

Answer 43

Using an example: if ft = 10 - 10 euros for 1 dollar
If et+1 = 14
The payoff is et+1 - ft = 4
So if I purchase a dollar forward now, I pay 10 for something that is worth 14 now and sell it immediately.

Question 44

Answer 44

According to UIP, beta must be 1 and alpha is zero. Empirical tests show beta is less than zero. When the domestic interest rate is high, its currency tends to appreciate instead of depreciate. This means we get a wrong prediction for next year’s spot rate, so the forward rate is biased.

Question 45

WHy does PEH predict b = 0?

Answer 45

PEH says that holding period returns on all bonds should be equal. There should be no excess returns and nothing should be able to predict excess returns. So b = 0

Question 46

Answer 46

Yes, average holding period returns are about the same as predicted by PEH.

Question 47

Answer 47

This shows returns from borrowing in yen and investing in higher interest rate countries. Doing this over times makes money, but there are lots of fluctuations. According to UIP, there should be no returns to this strategy

Question 48

Answer 48

The 3.29 shows the average returns from investing in high interest-rate countries. You borrow in dollars and invest in those with highest interest rates. The forward discount is the average interest rate differential between the high-interest rate countries and the dollar interest rate. The average annual change is the spot rate of the high interest currencies. The net return from the carry trade is the interest differential less the average rate of depreciation of the high-interest rate currencies. This is 17.24-13.95 = 3.29 =3.29

Question 49

Answer 49

Question 50

b

Answer 50

Question 51

Answer 51

Question 52

Answer 52

Question 53

Answer 53