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venture capital and the finance of innovation
Questions and Answers of
Venture Capital And The Finance Of Innovation
Using Table 7.3 and linear interpolation in discount factors, for a \(\$ 1 \mathrm{M}\) 1 -year swap with semiannual fixed rate of \(4 \%\) per annum and quarterly floating leg based on 3-month
Using the same setup as Example 2(a) Compute today's value of each of the four floorlets for a \$1M 1-year forward start 1 -year \(K=4 \%\) quarterly floor on 3 -month rates.(b) Compute today's value
Using the data in Table 7.3(a) Compute the semiannual forward swap rate for a 1-year swap, 2 -year forward, \(F_{2,1}\).(b) Using Black's normal formula with \(\sigma_{N}=0.80 \%\), compute the value
Let \(R, P\) be the value of a European receiver, payer swaption with the same expiry, swap term, and strike \(K\).(a) Let \(S\) be the value to the receiver of the underlying swap with fixed rate
Using the Black's normal call formula(a) Show that the delta of a call option, \(\partial C(0) / \partial A(0)\), equals \(N(d)\).(b) Using put-call parity, compute the delta of a put option.(c) What
Consider an ATMF straddle's price under lognormal and normal dynamics, and use the first central difference approximation\[N^{\prime}(x) \times x \approx N(x / 2)-N(-x / 2)\]to relate the normalized
Using the example in Figure 7.7 and the results in Table 7.5(a) Show the computations for the \(T_{1}\) discount factor curves in each of the \((u, d)\) states starting from the \(T_{2}\) discount
A Bermudan cancelable swap allows the owner to cancel a swap at some point before the swap maturity. The cancellation option is economically equivalent to a Bermudan swaption into an offsetting swap.
Use the Binomial Formula\[(a+b)^{n}=\sum_{k=0}^{n}\left(\begin{array}{l}n \\k\end{array}ight) a^{k} b^{n-k}\]to show(a)\[e=\lim _{n ightarrow \infty}\left(1+\frac{1}{n}ight)^{n}=\sum_{k=0}^{\infty}
Using an annual interest rate \(r=4 \%\), recompute Table 2.1 for \(F V(T)\) for a horizon date of 6 months, \(T=0.5\). Repeat for a horizon date of \(1 \mathrm{y}\) and 6 months, \(T=1.5\).Table 2.1
How long does it to take to double your money at a given rate \(r\) ? Begin with\[F V=P V e^{r t}=2 P V\]and approximate \(\ln (2) \approx 0.72\) to come up with the Rule of 72 .(a) At \(3 \%\),
Let \(r_{m}\) be the interest rate with \(m\) compoundings per year, for example, \(m=12\) means monthly compounding.(a) Derive the formula to convert \(r_{m}\) to \(r_{n}\) for general \(m,
A 2 -year semiannual coupon bond is issued on \(1 / 1 / 2020\) and matures on \(1 / 1 / 2022\) with a semiannual coupon rate of \(4 \%\) per annum and coupon dates 7/1/2020, 1/1/2021, 7/1/2021,
Geometric Series (a) In a Fractional Reserve system of banking, each bank need only keep a fraction αα, say 5%5%, of its deposits and can lend out 1−α1−α. The loan recipient will then deposit
Using the bisection method, compute the semiannual yield of a 5-year bond paying a semiannual coupon of \(2 \%\) per annum and trading at \(98 \%\). Start with bracketing levels of \(0 \%, 10 \%\),
Using a semiannually compounded yield of \(4 \%\) p.a., numerically or via evaluating the formula, compute the PV01 of(a) \(\$ 1\) million 5 -year zero-coupon bond(b) \(\$ 1\) million 5 -year \(4
For a \(T\)-year zero-coupon bond with continuously compounded yield \(y\), compute(a) Its modified duration, \(1 / P \times d P / d y\)(b) Its convexity, \(d^{2} P / d y^{2}\)(c) The price, modified
Limits at \(y=0\)(a) Evaluate \(P(C, y, N, m)\) (Formula 2.5) at \(y=0\).(b) Evaluate \(d P / d y\) (Formula 2.9) at \(y=0\).(c) Evaluate \(d P / d C\) (Formula 2.10) at \(y=0\).
Convexity(a) If \(f^{\prime \prime}\) exists, use the definition 2.11 and\[f^{\prime \prime}(x)=\lim _{h ightarrow 0} \frac{f(x+h)+f(x-b)-2 f(x)}{h^{2}}\]to show that \(f^{\prime \prime}(x) \geq 0\)
For a 30 -year monthly level-pay home mortgage loan of \(\$ 500,000\) with a \(3 \%\) interest rate(a) Compute the monthly level payment.(b) What is the total amount of interest you pay during the
Derivation of \(S(x, m, N)\)(a) Derive the formula for \(S(x, m, N)=\sum_{n=m}^{N} n x^{n}\) in Formula 2.16. Hint: Begin by evaluating \(S(x, m, N)-x S(x, m, N)\).(b) Alternatively, derive the
Let a 2 -year bond with a semiannual coupon rate of \(2.25 \%\) p.a. have a semiannual yield of \(2 \%\) p.a., and a 10 -year bond with a semiannual coupon rate of \(2.5 \%\) p.a. have a semiannual
Given instruments in the following table(a) Extract the semiannual discount factors for 10 years using the bootstrap method with linear and log-linear interpolation in discount factors.(b) On the
Using the price-yield Formula 2.5 for a bond with a periodic coupon of \(C / m\) with \(N\) remaining coupons, show that \(P(N, m, C, y) \times(1+y / m)^{N}\) equals the sum of all coupon payments
U.S. Treasury Bills are quoted based on an Act /360/360 discount yield, PB=PB= 1−yBN/3601−yBN/360, where NN is the number of days from settlement date to maturity date. (a) Provide a formula for
Compute price \(P\), sensitivity \(d P / d y\), convexity \(d^{2} P / d y^{2}\) of \(2 \mathrm{y}, 5 \mathrm{y}\), \(10 \mathrm{y}, 30 \mathrm{y}, 100 \mathrm{y}\) bonds, all with a semiannual coupon
Compute total interest for a level pay loan, \(I=\sum_{n=0}^{N-1} I_{n}\), to show that \(I=A L \times C / m\). Does this make sense?
Evaluate Formula 2.18 when \(s=1\), and explain the result.
For a given time series \(x_{1}, x_{2}, \ldots\), the \(N\)-period arithmetic Moving Average (MA), \(A(n, N)\), is defined as\[A(n, N)= \begin{cases}\left(x_{1}+\ldots+x_{n}ight) / n & \text { if } n
Milton Friedman famously said that changes in money growth affect the economy with “long and variable lags.” That means that if the government increases growth in the monetary base this month,
One of the reasons it’s difficult to be a monetary policymaker is because it’s so hard to tell what’s actually going on in the economy. It’s a lot like being a doctor in a world before
Complete the following sentences: With a real shock, when real growth is worse than usual, inflation is _______________ than usual. With an aggregate demand shock, when real growth is worse
Define the following:a. The monetary base, MBb. M1c. M2
Does the House of Representatives get to vote on who becomes the chairperson of the Federal Reserve Board? If not, who does get to vote?
Using the FRED economic database (https://fred.stlouisfed.org/), graph the Effective Federal Funds rate from 2007 to the present. Now click Edit Graph and then Add Line. Add the Unemployment rate.
Central banks and voters a like usually want higher real growth and lower inflation. What kind of shock makes that happen?
Let’s reenact a simplified version of the 1981–1982 Volcker disinflation. Expected inflation and actual inflation are both 10%, real growth is 3%, and to keep it simple, velocity growth is zero.
a. Suppose that the central bank follows a fixed 3% annual monetary growth rule, as Milton Friedman sometimes recommended. In the short run, what will the velocity shock do to real growth and to
Practice with the best case: You are the central banker, and you have to decide how fast the money supply should grow. Your economy gets hit by the following AD shocks and your job is simply to
Consider the following figure. Suppose that there’s a rise in →v due to business optimism—what Keynes called the “animal spirits” of investors. This pushes us to AD(2). If the
a. Do most federal government transfers of cash go to the elderly or to the poor?b. Do most federal government purchases of health care go to the elderly or to the poor?
Using the FRED economic database (https://fred.stlouisfed.org/), create a series showing federal expenditures as a share of GDP. First find Federal Government current expenditures. Then Edit Graph
Let’s take a look at one aspect of the U.S. tax system over the past 100 years. Using the FRED economic database (https://fred.stlouisfed.org/), look for “U.S Individual Income Tax: Tax Rates for
There are many ways to help poor people in foreign countries. You can find charities, for example, that will buy a cow or shoes for people in poverty or help to dig a well in a low-income village.
Assume that the economy is growing steadily and hasn’t had a recent recession. A new administration increases spending on the military by $200 billion, a significant amount.a. What is your estimate
What shifts AD to the left: A rise in taxes or a cut in taxes? Does this push →v up or push it down?
Let’s see what the “three difficulties with using fiscal policy” look like in real life. Categorize each of the following three stories as either (1) crowding out, (2) magnitude, or (3) a
When people “buy government bonds,” are they borrowing money or saving money?
Imagine you live in the land of Ricardia, where every citizen is a Ricardian and thus “Ricardian equivalence” is 100% true. Government spending never changes in Ricardia: It’s a fixed amount
If the U.S.-debt-to-GDP ratio were 100% and if the interest rate on the debt were 5% (not far from the truth at present), then what fraction of U.S. GDP would go toward paying interest on the debt?
Which of the following government policies are “automatic stabilizers” for the economy?Unemployment insuranceTemporary tax cuts that Congress passes when bad economic news hitsTemporary spending
We discussed three situations where fiscal policy is most likely to matter (though fiscal policy is best when all three are true):1. When the economy needs a short-run boost2. When the problem
In this question we will look at one of the automatic stabilizers, unemployment insurance. Using the FRED economic database (https://fred.stlouisfed.org/), search for unemployment insurance. You
Let’s examine the U.S. balance of trade (Exports-Imports) as we did in Problem 1, but this time we will do so as a percent of GDP. Using the FRED economic database (https://fred.stlouisfed.org/),
In the chapter, two stories about the deficit are told: “the great place to invest” story and the “foolishly saving too little” story. In the following examples, which is more like the
a. According to Table 1, how many Japanese yen could you get for 1 dollar in May 2017? Use the currency converter on Yahoo! Finance to find out how many yen you could buy for a dollar today. b.
According to the purchasing power parity theorem, what must be approximately equal across countries: the nominal exchange rate or the real exchange rate?
Which international financial institution focuses on the long-run health of developing countries: the IMF or the World Bank? Which one focuses on short-run financial crises in developing
Let’s translate between newspaper jargon about exchange rates and the economic reality of exchange rates. a. Last week, the currency of Frobia was trading one for one with the currency of
a. When the Japanese government slows the rate of money growth, will that tend to strengthen the yen against the dollar or weaken the yen against the dollar? b. When the Japanese government
Practice with the current account: Which of the following tend to raise the value of Country X’s current account? a. Country X sends cash to aid war victims in Country Y. b. Investors
Practice with the capital account: Which of the three categories of the capital account does each belong in? Which of the following tend to raise the value of Country X’s capital account? a. A
Let’s translate “Americans are foolishly saving too little” into a simple GDP story. Recall that GDP = C + I + G + Net exports. GDP is fixed and equal to 100 throughout the story: After all,
Let’s translate “The United States is a great place to invest” into a simple GDP story. Recall that GDP = C + I + G + Net exports. In this story, foreigners build up the U.S. capital stock by
Now that we’ve built up some intuition about exchange rates, let’s apply the principles more thoroughly. In this question, we discuss the U.S.–China exchange rate. Officially, the Chinese
The market for foreign currencies is a lot like the market for apples or cars or fish, so we can use the same intuition—as long as we keep reminding ourselves which way is “up” and which is
Corey, a young entrepreneur, notices that cigarette lighters sell for only $0.50 each in Utah but they sell for $1.00 each in Nevada.a. If Corey wants to make money by buying and selling lighters,
At Christmas, five-year-old Gwen runs a massive trade deficit with her parents: She “exports” only a wrapped candy cane to her parents, but she “imports” a massive number of video games,
A supply and demand model can illustrate the difficulty of keeping a fixed exchange rate: It’s much the same as any other price floor. Consider the following fixed exchange rate. Sparta uses a
Consider two equally wealthy families: one family lives in a relatively poor country and the other lives in a relatively rich country. Which family is more likely to own a mechanical dishwasher? Why?
In our basic model, a rise in money growth causes currency depreciation: We also know from our chapter on Business Fluctuations and the chapter on Monetary Policy that a rise in money growth normally
In Panama, a dollarized country, a Big Mac is about 30% cheaper than in the United States. Why?
Let’s look at the U.S. to U.K. foreign exchange rate using the FRED economic database (https://fred.stlouisfed.org). Search for US/UK Foreign Exchange Rate then change the beginning date to Jan 1,
We have said that services are likely to be cheaper in poorer countries, but is this true for all kinds of services? Can you think of some services that are more likely to sell for similar prices
According to Thomas Jefferson, how are ideas like flames?
In the following cases, will real growth rise, fall, or remain unchanged?Expected inflation = 5%Actual inflation = 7%Expected inflation = 3%Actual inflation = 1%Expected inflation = 6%Actual
a. What does a negative real shock do to inflation: Does it rise, fall, or remain unchanged?b. What does a negative real shock do to spending growth: Does it rise, fall, or remain unchanged?c. What
Are “real shocks” negative shocks, by definition?
When inflation rises, does the Solow growth rate rise, fall, or remain unchanged?
Let’s sum up some basic facts about the link between unemployment rates and recessions. Notice that the shaded bars indicate periods of recession, and wider bars mean longer
Recall that Y = C + I + G + NX. a. If government spending increases then we model that as an increase in:i. v.ii. M.iii. Q.iv. T.b. An increase in G shifts the AD curve:i. inwards.ii.
During the Great Depression, which of the following were mostly aggregate demand shocks and which were mostly negative real shocks? The fall in the growth rate of moneyThe fall in farm
Complete the following sentences: With a real shock, when real growth is worse than usual, inflation is _______________ than usual. With an aggregate demand shock, when real growth is worse
In the following cases, will real growth rise, fall, or remain unchanged?Expected inflation = 5%Actual inflation = 7%Expected inflation = 3%Actual inflation = 1%Expected inflation = 6%Actual
Are “real shocks” negative shocks, by definition?
When inflation rises, does the Solow growth rate rise, fall, or remain unchanged?
Let’s sum up some basic facts about the link between unemployment rates and recessions. Notice that the shaded bars indicate periods of recession, and wider bars mean longer
Using the FRED economic database (https://fred.stlouisfed.org/), let’s compare employment in manufacturing and construction. First, find manufacturing employment and then click Edit Graph and Add
Overall, labor force participation rates have been declining in the U.S. economy but not for every demographic. Let’s examine the labor force participation rates of teenagers and older people.
Using the FRED economic database (https://fred.stlouisfed.org/), find the “Youth Unemployment Rate in the United States” then click Edit Graph and Add Line and find the “Youth Unemployment Rate
Let’s examine the labor force participation rates of teenagers. Using the FRED economic database (https://fred.stlouisfed.org/), search for “Labor force participation rate 16 to 19 years.”
Goldin and Katz looked for the link between birth control and women’s labor force participation by examining the difference between states that acted early to make birth control legal and states
If you have to pick a country to lose your job in, and you know you’re going to be out of work for one year, which country offers the highest one-year average replacement rate? Which offers the
Let’s see how many jobs have to be destroyed for one net job to be created. As noted in the text, millions of jobs are created and destroyed every month. Suppose that 5 million jobs are
About how big is the difference in labor force participation rates between countries with the highest implicit tax rate on older men compared to countries with the lowest implicit tax rate? Round to
Let’s look at how the unemployment rate changes during and after a typical recession. Does the unemployment rate tend to reach its peak during the recession, or does it usually reach its peak
Let’s connect the minimum wage model back to the supply and demand model of the chapter on Price Ceilings and Price Floors. Is a minimum wage a price ceiling or a price floor? Does it create a
If we count “discouraged workers” as unemployed when calculating the unemployment rate, does the rate more than double, less than double, or remain unchanged?
Let’s compare 10-year corporate bonds and 10-year government bonds (called Treasuries). Go to the FRED economic database (https://fred.stlouisfed.org/) and search for “10 year corporate bond high
One type of debt that you may be familiar with is student loan debt. Using the FRED economic database (https://fred.stlouisfed.org/), search for student loans, then click on “Student Loans Owned
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