Research paper

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Question 1: Quantitative Strategies (20 marks)
(A) (7 marks) You observe that stocks with low price to dividend ratios in January
consistently deliver high returns over the following year compared to other stocks.
(i) Give a rational (risk based) explanation for this
If risk is time varying returns should be too. Stocks with low price to dividend ratios may
simply be stocks with higher risk, therefore they should have higher expected returns
(ii) Give an alternative explanation
It could be that there are no risk differences between these stocks and other stocks, however
investors just get really excited about some stocks and ignore others. The ones they ignore
will fall in price, but eventually investors will realize these stocks are not bad and they will
have to rise back up in price
(B) (7 marks) After sorting all stocks on characteristic X you form four portfolios with the
following alphas:
Low X 2 3 High X
-1.26% -0.28% 0.37% 1.35%
(i) Explain the relevance of alpha and what trading strategy you would employ.
We should always control for risk, otherwise the high return stock might turn out to just be a
high risk stock. One way to control for risk is to calculate alpha, which is the remaining
return after accounting for any of the security’s risk. In this case going long in high X stocks
and short in low X stocks seems like a good strategy.
(ii) You do the same for another characteristic Y and find the following result:
Low Y 2 3 high Y
-0.93% -0.18% 0.37% 0.92%
You also double sort on both X and Y and find the following alphas:
Low X 2 3 High X
Low Y -1.10% -0.33% 0.32% 0.82%
2 -1.20% -0.29% 0.34% 1.48%
3 -0.90% -0.20% 0.38% 1.07%
High Y -1.10% -0.24% 0.39% 1.21%
Can you improve on the trading strategy in (i)? Explain.
No we cannot improve on the strategy in (i). Even though high Y stocks appear to have higher
average returns than low Y stocks, it seems like this is simply due to a correlation with X.
Once we double sort on X and Y it is clear that differences in Y do not result in differences in
returns once we have controlled for X. Trading on Y will simply increase our transaction
costs without delivering better returnsPage 2 of x
(C) (6 marks) Briefly discuss momentum and post earnings announcement drift.
Momentum: stocks that did well relative to other stocks over the past year continue to do well
over the next year. Stocks that did poorly continue to do poorly. There is a reversal after
about a year.
PEAD: stocks that received a positive earnings surprise did well in the 3 months prior to the
earnings announcement and continue to do well over the next 6 months. While this looks like
momentum, and is indeed related to momentum, it is an independent effect which can be seen
by double sorting. Page 3 of x
Question 2: Venture Capital (40 marks)
It is currently 2011, Tom’s Rhinoplasty LLC, a young medical practice, has submitted the
cash flow projections below to Cartmen Venture Capital. All numbers are in millions.
Assume that there are no taxes. The appropriate discount rate for Tom’s Rhinoplasty is 15%
per year.
As can be seen from the cost and revenue projections, revenues will be minimal for the first
several years, while costs will be significant. Tom projects to become consistently profitable
after 2015. The capital expenditures row shows that Tom also plans to spend $1 million to
buy an office in 2011 and then another $4 million to buy the newest medical equipment.
INCOME STATEMENT 2010 2011 2012 2013 2014 2015 2016
Revenues 0 0 0 0 2.0 6.0 11.0
Expenses 0.0 2.0 3.0 4.0 5.0 7.0 7.0
Operating 0 0.5 1.5 2.5 3.5 5.0 5.0
Administrative 0 0.5 0.5 0.5 0.5 1.0 1.0
Other 0 0 0 0 0 0 0
Depreciation 0 1.0 1.0 1.0 1.0 1.0 1.0
Operating Income (EBIT) 0.0 -2.0 -3.0 -4.0 -3.0 -1.0 4.0
Interest Expenses 0 0 0 0 0 0 0
Interest Income 0 0 0 0 0 0 0
Income Taxes 0 0 0 0 0 0 0
Net Income 0.0 -2.0 -3.0 -4.0 -3.0 -1.0 4.0
CASH FLOW STATEMENT 2010 2011 2012 2013 2014 2015 2016
Net Income 0.0 -2.0 -3.0 -4.0 -3.0 -1.0 4.0
Operating Activities 0.0 1.0 1.0 1.0 1.0 1.0 1.0
Depreciation 0 1.0 1.0 1.0 1.0 1.0 1.0
Decrease in A/R 0 0 0 0 0 0 0
Increase in A/P 0 0 0 0 0 0 0
Decrease in Inventories 0 0 0 0 0 0 0
Cash Flow from Operations 0 -1 -2 -3 -2 0 5
Capital Expenditures and
Investment 0 1.0 0 4.0 0 0 0
Financing Activities 5.0 8.0 -5.0
Dividend 0 0 0 0 0 0 5
Sale of Stock 5 8
Increase in Debt 0 0 0 0 0 0 0
Net Increase in Cash 3.0 -2.0 1.0 -2.0 0.0 0.0
Cash Balance 0.0 3.0 1.0 2.0 0.0 0.0 0.0
(A) (7 marks) Fill in the rows Expenses, Operating Income, Net Income, and Cash Flow from
Operations. Briefly discuss the role of depreciation in calculating the available cash flow.
Does it play a role in this problem?
Expenses=Operating+Admin+Other+Depreciation
EBIT=Revenue-Expenses
Net Income = EBIT (because no taxes or interest)
Cash Flow from Operations = Net Income + DepreciationPage 4 of x
Depreciation is only there for tax purposes, it gets subtracted from income when calculating
the tax and then added back on to get cash flows. Here it plays no role since there are no
taxes.
(B) (6 marks) Because the firm has negative cash flows (as well as capital expenditures) early
in its life, it will need to raise equity. In 2013 it will approach a later stage VC to raise $8
million in equity financing. Today (in 2011) it is approaching Cartman for $5 million in
initial equity financing. Use this information to fill in the appropriate cells in the cash flow
statement.
There should now be a $5 million in 2011 financing activities and $8 million in 2013
financing activities
(C) (7 marks) Assume that cash earns no interest. Given information you have on cash flows,
capital expenditures, and financing activities, fill in the cash balance row. Show that if the
firm raises financing as in (B), its cash position will never go negative and will be exactly
zero in 2016. Starting in 2016 the firm will pay out all cash flows from operations as
dividends and will maintain a cash balance of zero. What is the dividend in 2016?
Net Increase in Cash=CF from Op – CapEx + Financing Activties
Note that Financing Activities are zero in 2012, 2014, 2015; $5m in 2011 and $8m in 2013.
We can use Net Increase in Cash to calculate the Cash Balance:
Cash Balance (t) = Cash Balance (t-1) + Net Increase in Cash (t)
In 2016, dividend must be such that the cash balance is zero. Since the cash balance is zero
in 2015, dividend is simply equal to CF from Op which is $5 million
(D) (6 marks) Tom projects that after 2016 dividends will grow at 3%. Use the Gordon
Growth Model to calculate the terminal value of the firm as of 2015.
TV(2015)=5/(r-g)=$41.7
(E) (7 marks) Calculate the stake that must be promised to the 2nd stage (2013) VC?
Hint: What cash outflows will he see? What cash inflows will he see?
Discounted to 2013, the value of the firm is 41.7/(1+r)2=$31.5 million
The fraction offered to the 2nd stage VC is 8/31.5=25.4%
(F) (7 marks) Calculate the stake that must be promised to Cartman VC in 2011?
Hint: What cash outflows will she see? What cash inflows will she see?
Discounted to 2011, the value of the firm is 41.7/(1+r)4=$23.8 million
Out of this, 25.4% is already promised to the 2nd stage VC, therefore 23.8*(1-.254)=$17.8
million is available to be split between Tom and Cartman. Cartman’s stake in the firm is
5/17.8=28.13% (this is the stake in the 2011 firm, eventually his share of the firm will be
.746*.2813=21%Page 5 of x
Question 3: LBOs (25 marks)
For simplicity assume that the rates of return on debt and equity are equal (lets say 10% but
you do not actually need to use this number).
Ripe For Raid Inc has assets valued at $100 million. This value comes from the expected
present value of future cash flows. The firm has outstanding long term debt valued at $20
million.
(A) (5 marks) Draw left and right hand sides of the balance sheet and calculate the book
value of equity.
Assets are 100 and must equal liabilities. Equity=Assets-Debt=20
Old Capital
Structure LBO structure New Capital Structure
Improved
Performance
replaces old
liability structure
Assets Liabilities LBO Assets Liabilities Assets Liabilities
100 Equity Equity 10 100 Equity 10 110 Equity
80 Debt Debt 20
90 90 Debt
90
Debt
20
(B) (5 marks) An LBO fund plans to buy out this Ripe For Raid. The fund will raise $90 in
debt, $9 million in outside equity from limited partners and $1 million of the general
partner’s personal money as inside equity. As part of the buyout it plans to fully repay Ripe
for Raid’s existing debt. Draw the balance sheet and calculate the book value of equity.
Assets have not changed, old capital structure fully replaced by new. Now Equity=AssetsDebt=10
(C) (5 marks) Suppose the GP is able to improve the firm’s operating performance by (ie the
value of the underlying cash flows) by 10%. What is the value of the equity stake? By what
percent has the LBO’s investment increased in value?
Hint: Which parts of the balance sheet change? Which do not?
Debt now remains at 90 but assets grow to 110, thus equity is 110-90=20. This is a 100%
gain. Page 6 of x
(D) (5 marks) This simple numerical example showcased one widely discussed mechanism
through which LBO’s can add value. Discuss another major way in which LBO’s add value
for their investors.
High leverage allows for large tax breaks. A large part of the gain for LBO’s is simply
coming from increased tax breaks.
(F) (5 marks) Suppose there is an economic downturn which causes the firm’s operating
performance to fall by 10%. What is the value of the equity stake? By what percent has the
LBO’s investment fallen in value? Discuss the dangers of leverage.
Debt now remains at 90 but assets fall to 90, thus equity is 90-90=0. This is a 100% loss.Page 7 of x
Question 4: Real Estate (15 marks)
Discuss Mortgage Backed Securities. Describe what it is, how it is formed, and how/when its
owners are paid. Explain how you would figure out the price of an MBS. Why were these
securities considered safe? What bad assumptions were made by investors when they were
purchasing these securities pre-2007?
An MBS is a pool of loans. Each loan simply entitles its owner to all future interest payments
coming from that loan. The loan could be for a house, a car, or a television. These loans were
pooled together by banks to reduce idiosyncratic risk: any single loan may default leaving the
owner with nothing. For a large pool of loans we can estimate roughly how many will
default and know what the expected payout should be.
These loans were then split into tranches. For example, the riskiest tranche included the first
loans that would default. If no loans defaulted this tranche would be paid, if even a small
number of loans defaulted this tranche would take large losses. Because this tranche was
quite risky, it was sold for a low price and had a high expected return. It was sold to risk
tolerant investors such as hedge funds. Because the risky tranches took on first losses, this
made the lower (safer) tranches safer. They would only not be paid if all of the tranches
above them failed. Because these securities pooled risk and redistributed it to those who
wanted risk, they were considered safe.
To price this security we use the discounted present value approach. We can model each
mortgage and make an assumption about how likely each is to default and what the
correlation is. We can then calculate how likely it is for each tranche to be paid.
Unfortunately many bad assumptions were made when investors were pricing these
securities. In particular, they assumed that real estate prices are unlikely to fall and that low
historic correlations could continue even in a downturn. Furthermore, investors assumed that
the ratings agencies were pricing these securities correctly.