BCOR 3100 Past Answers

Suppose the government has a fixed amount of money to give, and it can only give money to one of the three populations. 1. Suppose the government's goal is to increase consumption as much as possible without regard to what is being consumed. Who should the government give the money to, and why? 2. Suppose the government's goal is to stimulate housing consumption as much as possible. Who should the government give the money to, and why?

1. If it does not matter what is consumed, the government should give money to the group that would create the most demand in the economy, that being the poorest citizens because MPC is the highest. 2. If it the government's goal is to stimulate consumption on housing specifically, the government should give money to the group that would be most likely to spend that money on housing. Based on the 2 MPCs calculated above, that would be the middle class.

Suppose that the current one-year Treasury-bill rate is 3.15%, and the current (annual) rate for a two-year Treasury security is 3.70%. According to the unbiased expectations theory, what should be the expected one-year rate 12 months from now?

4.25%

This question and the following question are related to lectures 11 and 12 on market (in)efficiency. In technical analysis, there is a pattern called "head and shoulders" (you can search it up online). Suppose it is true that, whenever the pattern occurs, stock prices tend to subsequently crash in a very predictable fashion and produce negative average returns. Please answer the following two questions. Is this consistent with the efficient market hypothesis? If yes, explain why. If not, explain which of the three forms of efficient market hypothesis is being violated, and why.

A prediction of EMH is that it is impossible to beat the market or consistently predict returns. If the head-and-shoulders pattern consistently predict negative returns, that is a violation of the efficient market hypothesis. More specifically, this is a violation of the weak form of EMH which predicts that one cannot use historical prices (on which "head-and-shoulders" is based) to predict returns.

Let's discuss the intermediary in an initial public offering (IPO) using trading terminology. In a best-efforts IPO (rather than firm commitment IPO), does the investment bank act as an agent/broker or a principal/dealer? (a) agent/broker (b) principal/dealer

Agent/Broker An agent/broker does not take any risk and merely searches for business opportunities. This is exactly what an investment bank does in a best-efforts IPO: it searches for buyers of the IPO but does not guarantee anything. In contrast, a principal/dealer directly takes risk, which is analogous to the case of a firm commitment IPO: the investment bank directly buys the IPO shares from the issuing company.

In the U.S., mortgage interest payments are tax-deductible. That is, a mortgage borrower can benefit by paying lower income taxes if she also pays a mortgage. Consider the mortgage lending market. How does the policy of allowing for mortgage interest tax deduction impact the demand and supply curves of mortgage lending?2 What about the impact on the equilibrium quantity of mortgage lending and the equilibrium mortgage interest rate?

Because borrowers can pay less income taxes due to this policy, they will be more willing to borrow. This would increase the demand for mortgages (shifting the demand curve to the right and/or up). According to the supply-demand diagram, this causes both equilibrium mortgage interest rate and the amount of mortgage lending to increase.

Which types of securities tend to be riskier for investors? (a) Money market is riskier (b) Capital market is riskier

Capital market is riskier capital market securities have longer maturities than money market securities, and fundamental value can change more over longer periods of time. For instance, consider very short-term debt (money market) and long-term debt (capital market). The former has a very low probability of default. The latter has more, because even for a high credit quality company, things may go wrong over the long term.

At year-end, a firm has assets of $100 and debts due of $120. In this situation, the stockholders must pay an additional $20 out of their own pocket to cover the short-fall. T/F?

False

Commercial paper is a short-term obligation of the U.S. government issued to cover government budget deficits and to refinance maturing government debt. T/F?

False

In a defined benefit plan, the retirement benefit will vary according to rates of return on pension fund reserves. T/F?

False

The major asset of the Federal Reserve is currency and the major liability is U.S. Treasury securities. T/F?

False

The process of a securities firm creating a secondary market through buying and selling on its own account for securities or contracts is termed brokerage (or agency trading). T/F?

False

Suppose there is a continued stream of sell market orders sent to an exchange. This will cause the mid price to:

Go down

It is generally ____________ to find trading counterparties in over-the-counter markets than exchange markets. (a) Easier (b) Harder

Harder On exchanges, all market participants gather and submit their trading interests to a central place. In contrast, in over-the-counter markets, market participants are dispersed and one will have to search for others with offsetting trading interests.

In the U.S., most mortgage repayments are guaranteed directly or indirectly by the Federal government. That is, if you are an investor (lender) in the mortgage market, you don't have to worry about the mortgage borrowers defaulting. In case of a default, the government will pay you. How does this impact the supply curve, demand curve, as well as equilibrium quantity and equilibrium interest rate in mortgage lending?

If the federal government pays lenders in case of default, this massively reduce the risk for lenders. This policy makes lenders more willing to lend and thereby increases the supply of loanable funds (the supply curve shifts to the right and/or down). This policy does not impact the demand curve. According to the supply-demand diagram, this causes equilibrium mortgage interest rate to decline and the amount of lending to increase.

Refer to question above Now suppose the manager is only compensated with managementfees but not performance fees. In other words, the contract is similar to thatused in mutual funds. Further assume that, if the manager receives the sameamount of expected payoff from two strategies, he prefers the one with lowerrisk. Which strategy would he choose?

If there are no performance fees, both strategies would have the same expected returns because the original amount of assets under management, the amount on which the management fees are based, would be the same. Assuming that the manager would then prefer the strategy with lower risk, he would choose strategy 1.

Refer to question above What do you learn from this exercise about how the structure ofthe hedge fund manager contract, relative to the structure of mutual fundmanager contracts, induces risk-taking incentives in fund managers?

It is important to be careful think about how fund managers are paid and the incentives the payment structure creates. While performance fee can 3incentivize managers to work hard to get higher returns, it can also give managers incentive to take more risk.

Treasury notes, Treasury bonds, and municipal bonds are default risk free. (a) Yes (b) No

No Municipal bonds are not default risk free.

What is being displayed on limit order books on exchange markets?

Only limit orders

Consider a U.S. company that makes planes. The company does all its manufacturing in the U.S. and pay its suppliers and employees a fixed number of US dollars. The company sells its planes in South Africa at a fixed price of South African Rands. The company's profits are all recorded in US dollars (after converting Rand into dollars). Suppose the US dollar suddenly depreciates against the South African Rand. How does this impact the profits (revenue minus costs) of the company in US dollar terms?

Profit in US dollars go up

Consider the U.S. and Japan. Does the following scenario violate the purchasing power parity theory of exchange rates? Price level in U.S.: $200/basket Price level in Japan: U10,000/basket Exchange rate: $1 = U50 Assume that the basket of goods are the same between U.S. and Japan. Pleasejustify your answer with calculations.

This does not violate PPP theory because real exchange rate equals 1. 𝑅𝑒𝑎𝑙 𝐸𝑅 = 𝑁𝑜𝑚𝑖𝑛𝑎𝑙 𝐸𝑅 × 𝐹𝑜𝑟𝑒𝑖𝑔𝑛 𝑝𝑟𝑖𝑐𝑒/𝐷𝑜𝑚𝑒𝑠𝑡𝑖𝑐 𝑝𝑟𝑖𝑐𝑒 = 1 𝑈𝑆𝐷/50 𝑌𝑒𝑛 × 10,000 𝑌𝑒𝑛 per 𝑏𝑎𝑠𝑘𝑒𝑡/200 𝑈𝑆𝐷 per 𝑏𝑎𝑠𝑘𝑒𝑡 = 1

Every quarter, new information about the profits of companies is announced to thepublic. Researchers have found a phenomenon called "post-earnings announcementdrift". That is, companies with better (or worse)-than-expected profit announce-ments not only have high (or low) stock returns when the announcement is releasedbut also continue to do so in the subsequent months. Therefore, a trading strategythat buys (or sells) stocks with better (or worse)-than-expected profit announce-ments can beat the market. Please choose the best answer from below. (a) This does not violate market efficiency. (b) This violates the weak form (and thus also the semi-strong and strong forms)of market efficiency. (c) This violates the semi-strong form (and thus also the strong form) of market efficiency. (d) This only violates the strong form of market efficiency.

This violates the semi-strong form (and thus also the strong form) of market efficiency. Earning announcements are public information. The semi-strong form of EMH predicts that one cannot beat the market using public information.

Momentum strategies are trading strategies in which traders buy stocks that recently had high returns and sell stocks that recently had low returns. Such strategies are said to be able to "beat the market". If so, which of the following is true? 1. This violates the semi-strong form (and thus also the weak form) of market efficiency. 2. This does not violate market efficiency. 3. This violates the weak form of market efficiency. 4. This violates the strong form (and thus also the semi-strong and weak forms) of market efficiency.

This violates the weak form of market efficiency.

Given all other factors are unchanged, households generally supply more loanable funds to the markets as their income and wealth increase. T/F?

True

If the FOMC (federal open market committee) wishes to stimulate economic growth, in their open market operations, they could purchase more U.S. government securities. T/F?

True

In a mutual organization such as a credit union, the depositors are owners of the institution. T/F?

True

In order to reduce inflation, the Federal reserve may choose to sell Treasury bonds in open market operations. T/F?

True

A best-efforts offering is one in which: 1. the investment banker acts only as a distribution agent 2. the bid-ask spread is exceptionally high, but the investment banker does his best to sell the issue anyway 3. the investment banker acts as a principal for the issuer 4. the underwriter bears the risk of an unsuccessful offering 5. the issue can only be privately placed

the investment banker acts only as a distribution agent

Open-end mutual funds guarantee (may choose multiple or none): 1. investors a minimum NAV 2. to redeem investor's shares daily upon demand at the prevailing NAV 3. to earn a rate of return promised in the prospectus 4. investors a minimum rate of return

to redeem investor's shares daily upon demand at the prevailing NAV

Suppose that the current one-year interest rate is 1R1 = 2%. Assume that the expected one-year Treasury bond rates over the following three years (i.e., years 2,3, and 4, respectively) as as follows: E(2r1) = 2%, E(3r1) = 3%, E(4r1) = 2.5% Suppose the unbiased expectations theory is true. Please solve for the currentannual rates for two-, three-, and four-year maturity Treasuries. (In the book, thenotation for these interest rates are 1R2, 1R3, and 1R4, respectively.)

𝐸(1𝑅2) = ((1 + 1𝑅1) × (1 + 𝐸(2𝑟1))^1/2 - 1 = (1.02 × 1.02)12 - 1 = 2% 𝐸(1𝑅3) = ((1 + 1𝑅1) × (1 + 𝐸(2𝑟1) × (1 + 𝐸(3𝑟1))^1/3 - 1 = (1.02 × 1.02 × 1.03)^1/3 - 1 ≈ 2.33% 𝐸(1𝑅4) = ((1 + 1𝑅1) × (1 + 𝐸(2𝑟1) × (1 + 𝐸(3𝑟1) × (1 + 𝐸(4𝑟1))^1/4 - 1= (1.02 × 1.02 × 1.03 × 1.025)^1/4 - 1 ≈ 2.37%

Suppose that the current one-year interest rate is 1R1 = 2%. Assume that the expected one-year Treasury bond rates over the following three years (i.e., years 2, 3, and 4, respectively) as follows: E(2r1) = 2%, E(3r1) = 3%, E(4r1) = 2.5% Suppose the unbiased expectations theory is true. Please solve for the current annual rates for two-, three-, and four-year maturity Treasuries. (In the book, the notation for these interest rates are 1R2, 1R3, and 1R4, respectively.)

𝐸(1𝑅2) = ((1 + 1𝑅1) × (1 + 𝐸(2𝑟1))^1/2 - 1 = (1.02 × 1.02)12 - 1 = 2% 𝐸(1𝑅3) = ((1 + 1𝑅1) × (1 + 𝐸(2𝑟1) × (1 + 𝐸(3𝑟1))^1/3 - 1 = (1.02 × 1.02 × 1.03)^1/3 - 1≈ 2.33% 𝐸(1𝑅4) = ((1 + 1𝑅1) × (1 + 𝐸(2𝑟1) × (1 + 𝐸(3𝑟1) × (1 + 𝐸(4𝑟1))^1/4 - 1= (1.02 × 1.02 × 1.03 × 1.025)^1/4 - 1 ≈ 2.37%

Assume the unbiased expectations theory (chapter 2, L-G 2-7) is true throughout this question. 1. The current one-year Treasury bill rate is 5.2 percent and the expected one-year rate 12 months from now is 5.8 percent. What should be the current rate for a two-year Treasury security? 2. Suppose we observe the following rates: 1R1 = 8%, 1R2 = 10%. What is the one-year interest rate expected one year from now, E(2r1)? 3. Suppose the yield curve is inverted (i.e., interest rates/yields of longer maturity Treasuries are lower than that of shorter maturity Treasuries). What does this imply about the expectation of the movement of short-term interest rates in the future? Will it go up, go down, or stay roughly unchanged?

1. 1RN = [(1 + 1R1)(1 + E(2r1))...(1 + E(Nr1)]^1/𝑁 - 1 1R2 = [(1 + 1R1)(1 + E(2r1)]^1/2 - 1 = [(1.052)(1.058)]^1/2 - 1 ≈ 5.5% 2. 1R2 = [(1 + .08)(1 + E(2r1)]^1/2 - 1 = .10 1.10 = [(1 + .08)(1 + E(2r1))]^1/2 1.21 = (1.08)(1 + E(2r1)) 1.21/1.08 = (1 + E(2r1)) = 1.12037 E(2r1) ≈ 12.037% 3. If the yield curve is inverted, yields of longer maturity treasuries would be lower than for shorter maturity treasuries. Recall that the formula to calculate long-term yield is: 1RN = [(1 + 1R1)(1 + E(2r1))...(1 + E(Nr1))]^1/𝑁 - 1 If the longer-term treasuries have lower yields than shorter-term ones, this would imply that the short-term interest rate in subsequent years is expected to be lower than the current year. For example, if short-term interest rate increases over time, the calculation might look like part (a) above. If short-term interest rates decrease over time (5% 3% 1%), the calculation instead might look like this: 1R2 = [(1.05)(1.03)]^1/2 - 1 = 3.995% 1R3 = [(1.05)(1.03)(1.01)]^1/3 - 1 = 2.987%

Suppose there is one security being traded on an exchange where trading operates via a limit order book. The exchange opens at 9 am every day and closes at 4 pm. There is no uncertainty about the value of the security: each share is worth $10.5. Suppose there are two HFTs, 1 and 2, who compete by submitting limit orders. Other traders, collectively, submit one market order for one share every minute. Each market order buys or sells with equal probability. The goal of HFTs is to maximize expected profits. HFT profit calculation goes as follows: if my limit buy order of Q shares at a price $P is traded (met by a market sell order), my profit (possibly negative) is Q ×$(10.5 −P ). Symmetrically, If my limit sell order of Q shares at a price $P traded, then my profit (possibly negative)is Q ×$(P −10.5). The exchange rule says that the minimum tick size is $1, so limit orders can only be submitted at integer prices (...$8, $9, $10, $11, ...). When market orders arrive, the execution of limit orders follows the "price-time priority" principle. 1. Out of all possible prices, what is the lowest price at which HFTs are willing to sell (so that they will not suffer losses when trading)? What is the highest price at which HFTs are willing to buy? 2. Let's start thinking about how HFTs compete with each other. Suppose that the current limit order book only has limits orders already sub-mitted by HFT 1: limit buy orders of 1,000,000 shares at the price of $9 and limit sell orders of 1,000,000 shares at a price of $12. Now it is HFT 2's opportunity to submit limit orders. To make profits, at what prices should HFT2 submit limit buy and sell orders?

1. Because HFTs want to make a profit, they would not be willing to sell at any price lower than, or buy at any price higher than, the value of the share ($10.50), because otherwise they will lose money. Therefore, the answers to this question are $11 and $10. 2. Let's consider buy limit orders first. If HFT 2 submits orders at $9 or lower, her orders will never get executed. If her orders are below $9, HFT 1's orders are prioritized for having better prices. If her orders are at $9, because her orders are submitted *after* market marker 1's orders, her orders will also not be prioritized. Therefore, to make profits, HFT 2 has no choice but to submit limit buy orders at $10. Going through the same logic on the sell side reveals that HFT 2 will want to submit limit sell orders at $11.

Refer to above for this question Because HFTs are strategic — that is, they both take into account the behavior of the other when making their own decisions — in the end, both of them will end up submitting lots of limit orders at exactly the same bid and ask prices — the prices you solved in part (2). Since both HFTs submit at the same prices, "price priority" becomes irrelevant for who wins the business. "Time priority" becomes important. When limit order submission becomes possible (the market opens at 9 am each day),whoever can submit her limit orders before the other one — even if just by a split of a second — will get priority. However, because both HFTs have access to the same technology, none of them have an advantage over the other. Therefore, on half of the days, HFT 1 manages to be faster (and gets all the business on that day), while HFT 2 is faster the other half of the time. 1. Suppose HFT 1 can invest in colocation: by spending $100, she can move her trading firm to be at the same location as the exchange. As a consequence, when the exchange opens, her orders will be received 1 second earlier than the other HFT's orders. Is this a profitable investment? 2. Suppose HFT 1 has already invested in collocation. Now, supposeHFT 2 can also spend $100 to colocate, after which her orders will again bereceived earlier than HFT 1's orders with half chance, rather than always being1 second later. Is this a profitable investment for HFT 2?

1. By investing into colocation, HFT 1 can guarantee that he wins all the business on the exchange. This is a lot of profits: $0.5/share, and 1 share per minute. This means $30 profits per hour and $30 * 8 = $240 profits per day (assuming the market is open for 8 hours). Therefore, this profit more than justifies the $100 investment. 2. Yes. If HFT 2 does not make this investment, she gets zero profits because the other HFT 1 gets all the business. If she does, then they split the total profits half-half. From the calculations in part (c), this is still more than enough to justify the small $100 investment.

In class, we said that fiscal stimulus can happen in many ways such as direct investment, taxes cuts, etc. For simplicity, in this question, we will only consider the simplest type of policy which is to directly give people money — similar to the stimulus checks handed out by the U.S. federal government during COVID. The aspect we want to think about is who to give the money to. Suppose the U.S. population consists of poor people, middle-class people, and rich people. Suppose there are only three kinds of consumption: food, housing, and diamonds. Let's introduce a new concept called "marginal propensity to consume" (MPC). A person's MPC is defined as "how much one spends each additional dollar of income". For instance, if for every dollar of income given to me, I spend 70 cents, then my MPC is 70%. Please compute the MPC for the poor, the middle-class, and the rich using the information below. 1. For every dollar given to the poor, they spend 70 cents on food, 25 cents on housing, and save the rest. 2. For every dollar given to the middle-class, they spend 40 cents on food,40 cents on housing, and save the rest. 3. For every dollar given to the rich, they spend 5 cents on food, 15 cents on housing, 30 cents on diamonds, and save the rest.

1. For every dollar given to the poor, they spend 70 cents on food, 25 cents on housing, and save the rest. 𝑀𝑃𝐶= 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛/$1 = ($.70 + $.25)/$1 = 95% 2. For every dollar given to the middle class, they spend 40 cents on food,40 cents on housing, and save the rest. 𝑀𝑃𝐶= 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛/$1 = ($.40 + $.40)/$1 = 80% 3. For every dollar given to the rich, they spend 5 cents on food, 15 cents on housing, 30 centers on diamond, and save the rest. 𝑀𝑃𝐶= 𝑐𝑜𝑛𝑠𝑢𝑚𝑝𝑡𝑖𝑜𝑛/$1 = ($.5 + $.15 + $.30)/$1 = 50%

For simplicity, in this question, we will only consider bonds with one-year maturity and pays a single coupon at maturity with a coupon rate of 2%. Further, assume that you can invest any fractional number of dollars (e.g. $3,847.294910237593)into bonds. Before proceeding further, let me explain how TIPS payments adjust with inflation. Suppose you invest $100,000 into one-year-maturity TIPS with a 2% interest rate. Suppose inflation in the subsequent year turns out to be x = 5%. Then, the bond principal will be adjusted to $100, 000 ×(1 + 5%) = $105, 000, and your coupon payment will become $105, 000 ×2% = $2, 100. Your total payment one year later is going to be $105, 000 + $2, 100 = $107, 100. In contrast, payments from regular Treasuries do not adjust with inflation. For all questions below, your goal as an investor is to ensure that you receive no less than $10,000 one year from now in real terms. That is, if subsequent national inflation were x%, you want to receive no less than $10, 000 ×(1 + x%) payment next year under all scenarios.3 Suppose that the inflation rate next year will be x = 10% with 50% probability or x = 0% with 50% probability. You don't have a crystal ball so you don't know which scenario will happen. 1. Let's work out how much you have to invest to achieve your goal. - Suppose you can only invest in regular Treasuries (one-year-maturity, 2%coupon rate). How much money do you have to invest today to ensure that you achieve your goal? -Suppose you can invest in TIPS. How much do you have to invest to ensure you achieve your goal? 2. Do you see the benefit of TIPS relative to regular Treasuries in terms of protecting investors from inflation risk? Please explain.

1. Let p be the initial investment and x be the inflation rate. i. If investing in regular Treasuries, we need to consider the worse case: x = 10%. In that case, we need to receive $10,000 * (1 + 10%) = $11,000 one year later. Let's solve for p: p * (1 + 2%) = $11,000 -> p = $10,784.3 ii. If investing in TIPS, we need: $10,000 * (1 + x%) = [(p)(1 + x%)] + [(1 + x%)(p)(2%)] Divide both sides of the equation by 1 + inflation (x%) -> $10,000 = p + (2%)(p) Simplify -> $10,000 = (1.02)(p) -> p = $10,000/1.02 = $9,803.92157 2. Because TIPS adjust its payments with inflation, investors can be sure about the real payment they get when investing in TIPS and thus not worry about inflation. The same is not true about regular Treasuries. To guarantee a specific real payment, one will need to invest more into regular Treasuries. Further, the more volatile is inflation, the bigger the disadvantage of regular Treasuries.

1. Price levels are defined as the cost of a representative basket of goods and services that people purchase in their lives. We know: • Price level in the U.S. is $1000/basket. • Price level in the Eurozone is 800 Euro/basket. • Nominal exchange rate is 1.2 US dollars per Euro. Please solve for the real exchange rate between the two currencies, assumingthat the baskets are the same across the U.S. and the Eurozone. 2. The purchasing power parity (PPP) theory states that, whenever the real exchange rate is different from one, traders have incentives to buy goods from cheaper countries and sell them at higher prices in other countries. Assume it is feasible and low-cost to do so. Given your solution to part (a), what does the PPP theory predict will happen in terms of cross-country trading? Assuming that buying/selling currencies impact exchange rates, what will happen to nominal and real ex-change rates between Euro and U.S. dollar as a consequence of such trading?

1. Real Exchange Rate = Nominal Exchange Rate x 𝐹𝑜𝑟𝑒𝑖𝑔𝑛 𝑃𝑟𝑖𝑐𝑒/𝐷𝑜𝑚𝑒𝑠𝑡𝑖𝑐 𝑃𝑟𝑖𝑐𝑒 Real Exchange Rate = 1.2 𝑈𝑆𝐷/1 𝐸𝑈𝑅 × 800 𝐸𝑈𝑅 per 𝑏𝑎𝑠𝑘𝑒𝑡/1000 𝑈𝑆𝐷 per 𝑏𝑎𝑠𝑘𝑒𝑡 = 960/1000 = 0.96 In other words, goods are slightly more expensive (by 4%) in the U.S. relative to Eurozone. 2. PPP theory states that whenever the real exchange rate is different from 1, there is an incentive to trade goods internationally. In the problem above, a basket of goods is slightly more expensive in the U.S., so if there is little cost of cross-border commerce, people will buy the goods from Europe and sell in the U.S. to realize profits. An increased demand (supply) for goods in Europe (and U.S.) will lead to an increase in demand of Euro and a decrease in demand of US dollars. As a consequence, we expect US dollars to depreciate against the Euro to the point that real exchange rate equals one (at which point cross-border commerce will halt), and the purchasing power parity theory will hold true.

Consider one-year bonds issued by Pineapple Inc. If the company does not default, the bond will pay the stated interest plus principal back in one year. If the company does default — which happens with a 10% probability — then the company defaults on all bonds, and bond investors only get R fraction of the principal back (and none of the coupon). R is known as the "recovery rate". Suppose the company issues two types of bonds: senior and junior bonds. If bankruptcy happens, senior bondholders have higher recovery rates. 1. Suppose investors require an expected (average) rate of return of 5%. Suppose the recovery rates for senior and junior bonds are R= 70% and R= 30%, respectively. Assume bond interest rates are determined such that all bonds' expected returns exactly equal 5%. What will be the stated interest rates of the senior and junior bonds, respectively? 2. In general, do you expect the stated interest rate on senior bonds to be higher than, equal to, or lower than that of junior bonds? Why? Please justify your answer using explicit arguments.

1. Senior bonds: R% = 70% (would receive $70 for a $100 bond in the case of bankruptcy) Junior bonds: R% = 30% (would receive $30 for a $100 bond in the case of bankruptcy) Expected return: Senior bonds: (.1)($70) + (.9)(x) = $105 <- (5% return on $100 bond) $7 + .9x = $105 -> .9x = $98 -> x = $98/.9 = $108.89 The interest rate would have to be 8.89% Junior bonds: (.1)($30) + (.9)(x) = $105 <- (5% return on $100 bond) $3 + .9x = $105 -> .9x = $102 -> x = $102/.9 = $113.33 The interest rate would have to be 13.3% 2. As stated in the problem, senior bonds have a higher recovery rate than junior bonds. In other words, they receive higher returns than junior bonds if the company goes bankrupt. Thus, for the two types of bonds to have the same expected return, we would expect junior bonds to pay higher interest rates in non-bankrupt scenarios (because they pay less in bankrupt scenarios).

This question is related to lecture 20 and introduces the "money multiplier" — a concept that helps understand why there is so much debt in the economy. Suppose banks have a reserve requirement of 10%. That is, for every dollar of extra deposit a bank receives, it can (and will) lend out 90 cents. As explained in class, this money lent out will create more deposits. 1. Suppose bank 1 receives an additional $100 of deposits. How many additional dollars of loans are created by bank 1? 2. Now, suppose the loan made by bank 1 became deposits at bank2 who will then make more loans. How many additional dollars of loans are created by banks 1 and 2 combined? 3. Suppose this process goes on forever, to bank 3, bank 4, and ... bank infinity. How many additional dollars of loans are created by this infinite chain of banks?

1. The reserve requirement of 10% requires that banks keep 10% of this money on hand, so it would loan out 90% of this $100 ($90). 2. Continuing with the reserve requirement of 10%, bank 1, as described above, would loan out 90%, or $90 of the $100 deposit. If this $90 is deposited at bank 2 and this bank has the same reserve requirement of 10%, bank 2 would loan out 90% of the $90 deposit they receive from bank 1 (.90 x $90 = $81). In total, this money multiplier effect would create $90 from the first bank and $81 at the second, or $171. 3. Here, the reserve requirement of 10% means that 90% of the deposits banks receive would be loaned out and deposited to the next bank, so r = .90. The sequence looks like this: $90 + $81 + $72.90 + $65.61 + $59.05 + $53.14... sum can then be calculated using the formula a_1/(1-r) . This will then equal $90/(1-.90)=$900.

In the U.S., interest income is taxed. Let's assume the tax rate to be 30%.Then, if you lend $100,000 to someone and get paid $100,000 plus $10,000interest one year later (10% interest rate), you need to pay 30% ×$10, 000 =$3, 000 to the IRS. The remaining $7,000 is your take-home interest income. i. Suppose congress suddenly passed a law that increases interest income tax rate (e.g. from 30% to 50%). What is the impact on the demand curve of lending? What is the impact on supply curve? ii. Based on the supply-demand diagram (e.g., Figure 2-4 in the book), what would be the consequence of this law on the equilibrium quantity of lending and the (pre-tax) equilibrium interest rate?

1. The supply curve will contract (shift to the left and/or up). There are two possible ways to think it through and arrive at this answer. 1) If tax rate goes up, supplier of funds will be less willing to lend money at the same pre-tax interest rates. 2) For lenders to be happy to do the same quantity of lending, they will demand the same amount of post-tax profits. To achieve this, the pre-tax interest rate must increase. The demand curve is unchanged. 2. According to the supply-demand diagram, contraction of supply leads to a higher equilibrium interest rate and a lower equilibrium quantity of lending.

In money markets, investors trade securities that: (may choose multiple) 1. mature in one year or less 2. have little chance of loss of principal 3. must be guaranteed by the federal government

1. mature in one year or less 2. have little chance of loss of principal

First, consider a single standalone bank. Suppose it has $10 mil-lion in assets and $E million in equity, so the remaining $(10 −E) is debt. Let's define leverage defined as L = 10/E (asset-to-equity ratio). Asset value can change over time. For instance, if the bank's operations were more (or less) profitable, its asset value will go up (down). Suppose the value of the bank's assets next year has the following probability distribution: Asset Value (million) | Probability $7 | 5% $9 | 20% $11 | 50% $13 | 20% $15 | 5% Assume that the debt value of the bank does not change.4 What happens to the bank when asset value changes? Well, recall from your accounting class: if the bank's asset value goes up (down) by one dollar, its equity value will also go up (down) by one dollar. Also, the bank goes into bankruptcy if its asset value is equal to or lower than its debt value, which does not change. What is the probability that this bank will go bankrupt if it has a leverage of 10 to 1 (L = 10)? What if 5 to 1 (L = 5)?

Case of L = 10: L= A/E -> 10/E -> A=10; E=1; D=9 (A = D + E) Bankrupt when A ≤ D If assets drop to $9 million or below, the bank will go bankrupt. Based on the table provided, there would be a 25% chance of this happening (20% for A=$9 million + 5% chance for A=$7 million). Case of L = 5 is analogous: L= A/E -> 10/E -> A=10; E=2; D=8 (A = D + E) Bankrupt when A ≤ D If assets drop to $8 million or below, the bank will go bankrupt. Based on the table, there would be a 5% chance of this happening.

Which of the following would be considered fiscal stimulus? (a) Reducing tax burden of households. (b) Providing tax rebates to firms for hiring workers. (c) The central bank increasing money supply. (d) Increasing government expenditures on infrastructure projects.

Reducing tax burden of households, providing tax rebates to firms for hiring workers, & increasing government expenditures on infrastructure projects. Fiscal stimulus refers to increasing government consumption or transfers or lowering taxes. It focuses on the actions of the government, not the central bank, which makes monetary policy. Therefore, (a), (b), and (d) are fiscal stimuli. Choice (c) is a monetary stimulus.

Consider a hedge fund with initial assets under management (AUM) of $1 billion; the fund will operate for a year. The manager is paid by a standard "2+20" hedge fund contract. That is, at the end of the year, he collects management fees of 2% of AUM (as of the start of the year), and if the fund's return is above 0% (the hurdle rate), he collects 20% of that in performance fees. For instance, suppose the fund's return turns out to be 5%, which amounts to profits of $1 billion ×5% = $50 million in dollar terms. The manager then collects$50 million ×20% = $10 million in performance fees, in addition to the $1 billion ×2% = $20 million management fees. If the fund's return is below 0%, then the manager only collects management fees. Let us now consider the risk-taking incentives of the fund manager. Suppose the manager chooses between these two strategies: • Strategy 1 yields a sure return of 5% (no risk). • Strategy 2 yields a +20% return half of the time and a -20% return the other half of the time. Thus, it is a strategy with zero expected returns and much higher risk. Because investors like higher returns and dislike risk, strategy 2 is dominated by strategy 1 — that is, it is worse in terms of both risk and returns. Thus, if the manager chooses strategy 2, this is bad for investors. Please compute the manager's expected payoff under both strategies. (The selfish hedge fund manager will choose whichever strategy maximizes his expected payoff.)

Strategy 1: [ (5% return on $1B = $50,000,000) x 20% = $10,000,000 (performance fees)] + [($1B x 2%) = $20,000,000 (management fees)] = $30 million total Strategy 2: [20% return on $1B = $200,000,000 x 20% = $40,000,000 (performance fees)] + [($1B x 2%) = $20,000,000 (management fees)] = $60million[-20% return on $1B = no performance fees)] + [($1B x 2%) = $20,000,000 (management fees)] = 20million = (.5)($60 million) + (.5)($20 million) = $40 million

Recall the law of one price is the idea that securities (or baskets of securities) with identical payoff must have identical prices. In short, "the same thing must not have two different costs". Is there a violation of law of one price in the following scenario? There are three currencies, dollar ($), euro (€), and yen (U). You can easily convert one into another at the following exchange rates: $2 = €1; $1 = U100; €1 = U150. (Remember the transaction can go either way. For instance, you can convert any $X into €X/2, or any €X into $2X.)If you think there is no violation, please justify your answer with explicit calculations. If you think there is a violation, in addition to justifying your answer, please also construct a hypothetical trading strategy to take advantage of the violation.

The law of one price is violated because it is possible to obtain the same currency in two different ways at different costs. Possible arbitrage strategy: a. Borrow 1 USD and convert it into 100 Yen b. Convert that 100 Yen into 100/150 = 2/3 Euro c. Convert that 2/3 Euro into 23 × 2 = 43 ≈ 1.33 USD Thus, we can pay back the original 1 USD and have some (0.33 USD) leftover, so this is an arbitrage.

Recall that if markets are efficient, all price changes must be exactly justified by changes in fundamental value. Consider a company that makes bottles. The company can manufacture exactly a million bottles every year at the cost of $6/bottle and sell them at the price of$10/bottle. Assume there is no other cost or taxes. Assume that bottle prices never change and that the company can always sell all the bottles it manufactures. Thus, the company makes $4 million in profits each year.7 Further assume the company always pays out all its profits as dividends to shareholders.8Suddenly, the company experienced a surprising technology breakthrough that lowered the bottle production cost to $2/bottle. Assume this is the only change that happened. When this news was announced, the company's stock price immediately jumped by +50%. Does the market appear efficient? Why or why not? Make sure to backup your answer with calculations.

The market does not appear efficient. It is true that the price immediately responds to the information, but the amount of price movement is less than that justified by the change in fundamental value. The Efficient Market Hypothesis states that stock prices are the best estimates of the fundamental value of the stock. The fundamental value of the stock is related to how much the stock is currently, or may in the future, pay investors, which is then linked to a company's profits, and this must be true in order for prices to be considered "efficient." In the above scenario, the company started with a $4 profit/bottle ($10-$6). After implementing the new technology, the company's profits increased to 3$8/bottle ($10-$2). This should imply, in the absence of any other new information relevant to the fundamental value of the stock, that the price of the stock should increase, and would increase by double (100% increase, not 50%).

Common stocks typically have which of the following that bonds do not have? (a) Voting rights (b) Fixed cash flows (c) Set maturity date (d) Tax deductibility of cash flows to investors (e) Limited liability

Voting Rights & Limited Liability

On average, bank liabilities tend to have shorter maturities and greater liquidity than bank assets. (No need to explain your answer to this question) (a) Yes (b) No

Yes

An improvement in economic conditions would likely increase supply of loanable funds (shift the supply curve down and to the right). (a) Yes (b) No

Yes Because 1. Lenders (suppliers of loanable funds) are deciding whether to lend to entities (businesses, etc). If economic conditions improve, lenders may perceive the default risk to be lower, and thus be willing to lend more for the same interest rate, because expected returns (= interest rate - expected default losses) are higher. i. Students can get full credit if they point out that lenders are more "optimistic", or something along these lines. & 2. When overall economic conditions improve, lenders' economic conditions likely also improve and have more money to lend.

In order to reduce inflation, the Federal reserve may choose to sell Treasury bonds in open market operations. (a) Yes (b) No

Yes Selling Treasuries means that the Fed is decreasing the amount of money (currency and bank reserves) in the financial system.

Suppose mutual fund investors, on average, earn below-market post-fee returns in their mutual fund investments. Is it possible that mutual fund managers, on average, have skill to "beat the market"?

Yes, it is possible

Is there a violation of market efficiency in the following scenario? Company A owns 50% of company B. Company B's stock is valued at a total of $100 million. Company A's stock is valued at a total of $40 million.

Yes, there is a violation

Standard municipal revenue bonds are: 1. backed by the full taxing authority of the municipality 2. always offered with a best-efforts offering 3. collateralized by the earnings from a specific project 4. backed by mortgages 5. backed by the U.S. Treasury

collateralized by the earnings from a specific project