Explain how we calculate abnormal returns. Why would we want to look at abnormal returns?

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Question 1: Quantitative Strategies (20 marks)
(a) (6 marks) Explain how we calculate abnormal returns. Why would we want to
look at abnormal returns?
If we look at raw returns we don’t know if they are compensation for extra risk or true
profit. It is better to look at risk adjusted (abnormal) returns instead. To
calculate them you first need a “normal” return, for that one needs an asset
pricing model. For example with the CAPM the expected return on any asset
is Rf+B*(Rm-Rf) where B is that asset’s beta with the market. You first
compute the beta by regressing return on past returns, you then compute the
expected return on any day by using the market return on that day. The
abnormal return is the difference between the expected an actual returns.
(b) (6 marks) Suppose X and Y are different characteristics of financial assets (for
example size and past volatility). X and Y are positively but not perfectly
correlated.
I sort all firms based on X and form portfolios in which X is in lowest 20%, next
20%, … top 20%. For each portfolio I calculate alpha in percent per quarter:
X quintile: 1 2 3 4 5
alpha: -2 -1 0 1 2
Separately, I sort all firms based on Y and form portfolios in which Y is in
lowest 20%, next 20%, … top 20%. For each portfolio I calculate alpha in
percent per quarter:
Y quintile: 1 2 3 4 5
alpha: -1 -0.5 0 0.5 1
I then do a double sort where portfolio is in one of 5 X-quintiles and one of 5
Y-quintiles. X quintiles are on the vertical axis and Y quintiles are on the
horizontal axis. For each group I calculate alpha
Y
1 2 3 4 5
1 -2 -2 -2 -2 -2
2 -1 -1 -1 -1 -1
X 3 0 0 0 0 0
4 1 1 1 1 1
5 2 2 2 2 2
Explain what trading strategy you would form based on the above results.
Intuitively, what are the above results telling you?
From looking at the univariate results it looks like both X and Y are profitable since a
strategy long portfolio 5 and short portfolio 1 earns positive abnormal returns.
However, the double sort reveals that only X is profitable and that any Page 2 of 4
apparent profits in Y are simply due to its correlation with X. In particular, once
we hold X constant there is no difference between high Y and low Y portfolio.
The best trading strategy would isolate the effect of X by buying only X5 and
shorting X1.
(c) (8 marks) Describe the different tests you would do before implementing a trading
strategy such as in (b).
Students can discuss the following points. A good explanation of 3-4 is enough for
full marks:
-Ability to trade in real time
-Testing for risk
-Testing if strategy still profitable after transaction costs
-Testing if strategy is highly correlated with liquidity
-Testing if strategy is highly skewed or has a big value at risk
-Overfitting, in sample versus out of sample tests.
-Consistency of strategy in different time periods
Question 2: Venture Capital (30 marks)
(a) (20 marks) For simplicity this problem will be fully in present values without the
need to discount cash flows or consider interest rates.
You are aware that the demand for kosher pork is huge, with the present value of
future revenues being $100 million. To receive these revenues one would
need to build a pig farm which would cost $40 million.
There is one problem – a kosher pig has yet to be invented. After experimenting in
your garden, you may have found a way to turn pigs kosher. You estimate
that there is a 5% chance you are right and you will be able to raise kosher
pigs, and a 95% chance you are wrong. In order to test your theory, you will
need $1 million. You decide to ask your neighbor Angel Malach for this $1
million in return for an equity stake (call this year 1).
In year 2 you will find out if you are successful or not. In case you are successful,
you will approach Bin Halal Capital for the cost of the farm, they too will ask
for an equity stake. What fraction of equity will Angel Malach ask for in year
1? What fraction of equity will Bin Halal Capital ask for in year 2? What
fraction of equity will you be left with after year 2?
NPV as of end of 1: 60m
Post-Money value as of the end of 1: 100m
Bin Hallal stake: 40/100=40%
You + Angel stake: 60%
You + Angel value: 60m
NPV as of start of 1: -1+.05*60+.95*0=2
Post-Money value as of start of 1: .05*60=3
Angel stake: 1/3=33%
Your stake: 2/3=67%
After Bin Hallal contributes your stake goes down to (2/3)*60%=40%Page 3 of 4
(b) (10 marks) There are multiple ways in which firms can fund themselves. Very
briefly discuss the major ways in which firms tend to finance themselves.
Then discuss why some of these are inappropriate for younger firms and what
makes Venture Capital work particularly well for younger firms.
Firms can raise capital through debt (fixed promised payments) or equity (profit
sharing). Equity itself can be private or public. For young firms, debt does not
work well because it may encourage risk shifting, risk shifting is especially
severe for young firms because managers have lots of discretion at testing
new strategies. Furthermore, young firms tend to have little collateral and low
early cash flows so debt would have to carry high interest rates (expensive)
and be quite back loaded (possible but atypical). Public equity is also not a
good option because it requires a lot of expensive disclosure. Furthermore,
investments are quite illiquid which may not work for short horizon public
equity investors. This leaves private equity. Private equity does not encourage
risk shifting, is better at aggregating information because investors are big,
and is willing to stick around for the long run decreasing issues of illiquidity.
Question 3: LBOs (30 marks)
Consider a risk neutral world with a 10% discount rate and a 10% interest rate on all
risk free bonds. Earnings are $10m good years and $5m in bad years with
each having probability 0.5.
(a) (5 marks) Suppose the growth rate is 0%, calculate the value of the firm.
Using GGM: 0.5*(10+5)/0.1=75
(b) (4 marks) Suppose the firm has outstanding perpetual debt of $20m and that
there are no tax shields for debt. Calculate the value of the debt, the value of
the equity, and the enterprise value (debt+equity).
Nothing changes, the value of the debt is 20, the value of the equity is 75-20=55, and
enterprise value is 75.
(c) (5 marks) Suppose you buy the company for the price you solved for in (a) and
finance it fully out of your pocket (note that there is no debt). You are then are
able to raise the growth rate to 2%, what is your annual cash flow and the new
value of the firm?
Cash flow: 0.5*(10+5)=7.5
Using GGM: 0.5*(10+5)/(0.1-0.02)=93.75
(d) (6 marks) Now consider a world with a corporate tax rate of 20% (there are still
no personal taxes). What are the annual cash flows to you if you were to buy
the company described in (a) with no debt in the capital structure? What
would you be willing to pay for this firm?Page 4 of 4
Suppose you buy the firm for this price, then you take a $40m loan against the firm,
that is, the company undertakes a leveraged recapitalization. The equity sale
proceeds are then invested in government bonds at 10%, on your personal
account. Assume there are no personal taxes but there are corporate taxes of
20%. What is your total annual cash flow, the market value of the equity, the
market value of the debt, and the enterprise value (debt+equity) of the firm?
All equity: Your cash flows are (0.5*(10+5))*(1-0.2)=6. The value of this is 6/0.1=60
Levered: Your cash flows are now: (0.5*(10+5)-40*0.1)*(1-0.2)=2.8 from equity and
40*0.1=4 from debt for a total of 6.8. The present value of this is 68 where 40
is debt and 28 is equity.
(e) (5 marks) Use (c) and (d) to comment on the benefits of LBOs
LBOs raise value and profit in two possible ways. First they raise efficiency by cutting
waste, etc. This raises profit margins and potentially growth as in (d). Second,
they increase leverage and take advantage of tax shields as in (c)
(f) (5 marks) Discuss potential problems with LBOs
One major problem with LBOs is also the benefit: leverage. When a firm is highly
levered it has difficulty withstanding relatively small negative shocks. It will
then be subject to bankruptcy costs.
Question 4: Real Estate (20 marks)
(a) (7 marks) Briefly discuss the differences between fixed rate and adjustable rate
mortgages. Which would you take if you were particularly worried about high
future inflation?
In fixed rate mortgages the (nominal) interest rate is fixed and so monthly payments
are fixed. With an adjustable mortgage monthly payments depend on the
prevailing interest rate, for example Libor+2%, thus if Libor moves monthly
payments move. When inflation raises interest rates are likely to rise too. On
the other hand higher inflation increases the nominal value of your home
without increasing the nominal value of FRM payments, or in other words it
decreases the real value of FRM payments without decreasing value of home.
Thus FRM is better if borrower is particularly worried about inflation.
(b) (13 marks) Discuss securitization and Mortgage Backed Securities. Securitization
is blamed by some for the financial crisis, explain why.
Securitization is the packaging and subsequent reselling of mortgages into pools of
mortgages or MBS. An MBS is a pool of loans. Each loan simply entitles its
owner to all future interest payments coming from that loan. These loans were
pooled together by banks to reduce idiosyncratic risk: any single loan may
default leaving the owner with nothing. Page 5 of 4
Traditionally banks raised money from depositors and held onto the loans, forcing
them to be very careful at who to give loans to. With securitization banks were
able to sell these loans off to other investors. This was good as it increased
the potential pool of money which can be used for loans. However this also
reduced monitoring incentives for banks – since the banks were no longer
holding onto the loans, they became less careful. For still unexplained
reasons (perhaps lack of sophistication) the end buyers did not pressure the
banks to be more careful. This resulted in many bad loans being given out
and subsequently defaulting. Furthermore, because of high leverage, these
defaults resulted in bankruptcies and many bankruptcy costs