(SS 2016) Übungen PDF

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TUTORIAL 1 – ECONOMICS OF CRISES Baptiste Massenot 1. Define a credit crisis: Sharp reduction in lending because financial institutions face difficulties. 2. How does a credit crisis spread to the housing sector? Households cannot get credit and cannot buy houses. -> housing demand decreases -> house prices drop In case mortgages with adjustable rates, for example, some borrowers might not be able to repay, thus forcing them to sell their house. -> supply of houses in creases -> house prices further decrease 3. How does a credit crisis spread to the labor market? Firms cannot get credit and thus stop investing and hiring. 4. How does a credit crisis affect public finance? Higher unemployment implies that the state has to pay more social benefits. Lower economic activity means that the state gets less tax revenues. The state has to pay higher interest rates on its debt (e.g. because credit is scarcer or investors fear that the government won’t pay back), therefore further raising costs. Another cost is bailouts of large companies that may go bankrupt. Fiscal stimulus (e.g. subsidies to buy a new car) may further strain public finance. 5. Why is long-term unemployment more harmful than short-term unemployment? Long-term unemployment makes it harder to find a job and expected wages decrease. 6. What is the definition of a recession according to the NBER? Recession = GDP declines for at least 2 consecutive quarters. 7. GDP usually grows 3% per year. If the economy is hit by a crisis and GDP declines 5%, what is the income loss? 8%. 8. Assume that only 50% of the population is affected by the crisis. What is their income loss? 16%. 9. What is a bubble? Bubble = large and long-lasting deviation of an asset price from its fundamental value. 10. How does the fundamental value of an asset depend on the interest rate? Negatively. The interest rate tells you how much you discount future payments. The more you discount them, the lower the fundamental value. 11. The interest rate is 5%. You consider buying a house worth 100k$. What annual rental revenue would make you indifferent between buying the house or not? 5000$ of rental revenue make you indifferent with investing in bond.

12. Rents are 3k$ per year, interest rate is 0%, and you expect house prices to be 100k$ in one year. What is the fundamental value of a house that you plan to sell in one year? (all houses are the same) 103k$. 13. Assume the central bank conducts a contractionary monetary policy that increases the interest rate to 3%. What is the new fundamental value of the house? 100k$. Higher interest rates decrease the fundamental value and thus asset prices. 14. Based on extrapolation of historical data, you expect house prices to increase by 1% in one year. Interest rate is 5%. What is the fundamental value of a house that pays 10k$ of rental revenue per year and that you plan to sell next year? X = fundamental value, also the house price

=

,  ,

+

. ,

=> X = 250k$

Discount at the 5% rate! 15. What is the expected price increase is 3%?

=

,  ,

+

. ,

=> X = 500k$

When investors expect house prices to increase at a faster factor rate (e.g. became they extrapolate a histrorical trend), their willingness to pay for a house increases. 16. What if the expected price increase is 5%? With a 5% expected increase, the equation does not have a solution. The reason is that investors are now willing to pay any price. Whatever price you pay, you will get more than the interest rate. 17. In the latter case, what is likely to happen? Either house prices will not increase as much as investors expected, e.g. because supply will increase or because demand will not be high enough at such high prices. Alternatively, the interest rate will increase to make bonds attractive again (arbitrage argument). 18. Consider a one year treasury bond with a coupon payment of 10$ and a principal of 100$. The interest rate is 10%. What is the present value of the bond? 100 $. 110 $ payment you will get in 1 year 1,1 discounted by the interest rate 19. Consider a one year corporate bond with a coupon payment of 10$ and a principal of 100$. The interest rate is 10%. Based on historical data the company is expected to default with probability 1%. What is the present value of this bond? (assume linear utility) 99 $.

20. Assuming the bond trades at its present value, what is its return? With prob. 99%, you get 110. With prob. 1 %, you get 0 (the bond defaults) Return =

99 x 110 = 10 % 99 -> the price you paid for the bond

21. What is the risk premium? The spread is 0% since they yield the same return. This is because of linear utility, there is no risk premium investors are risk neutral. 22. If investors were risk averse, how would the risk premium vary with the probability of default? When investors become risk-averse, the risk premium will be positive and will increase with the probability of default. 23. Consider a one year mortgage backed security that is based on 2 1 year mortgages that each pay yearly interest payments of 10k$ for a house worth 90k$. Based on historical data, the probability of default of each of these mortgages is estimated to be 10% (the security is collateralized, only interest payments are lost). The safe interest rate is 5%. What is the present value of this MBS? 0.81 x 200k

+

2 x 0.09 x 190k +

0.01 x 180k

Prob. That no mortgages default: 0.9 x 0.9 = 0.81 prob. that only 1 mortgage defaults: 0.9 x 0.1 = 0.09 prob. that both mortgages default at the same time: 0.1 x 0.1 = 0.01 Expected payoff of the MBS: 198k Present value of the MBS = 198k / 1,05 = 189k 24. Now assume that borrowers always default together. What is the present value of the MBS? Expected payoff becomes: 0.9 x 200k + no mortgages are defaulting

0.1 x 180k = 198k both mortgages are defaulting

Resent value also stays the same = 198k/1,05 = 189k Conclusion: Whether risks are independent or correlated, does not affect the present value of the security. 25. What is the probability of making a loss in each case? Probability of loss is the probability that the payoff will be lower than 189 (assumed to be the price you paid for the security) -

Independent risk: Correlated risk:

1% 10%

TUTORIAL 2 – ECONOMICS OF CRISES Baptiste Massenot 1. Define leverage. Leverage is the amount of debt you use to purchase an asset. 2. You buy a 10k$ asset with 1k$ down payment and borrow the rest. What is your leverage? You are leverage 10 to 1. 3. What is your equity? Equity = Assets – Liabilities = 1k$ 4. Draw your balance sheet. Assets Asset: 10k

Liabilities 9k: debt 1k: equity

5. You buy the same house with the same down payment but you finance your down payment with another mortgage. What is your leverage? Leverage is infinity (equity is 0 and anything divided by 0 is infinity) 6. What is the typical leverage of a homebuyer? 5 to 1 (equivalent to a 20% down payment) 7. If you buy a house with a leverage of 10 to 1, by how much should the value of the house decrease to destroy all your equity? Equity is 10% of total asset value, so equity is destroyed id asset value decreases by 10%. 8. What if you are leveraged 30 to 1? Equity is now 1/30 = 3.3333% of asset value, so equity is destroyed if asset value decreases by 3.3%. When you are more leveraged, it takes a lower drop in asset value for your equity to be destroyed. 9. You buy a 1m$ house that rents for 50k$ per year. What is your annual return? 5%. 10. What if the value of your house drops by 10%? You still make 50k in rental revenue and you make a capital loss of 100k. Overall you lose 50k. Your return on investment becomes -5%. 11. What if you 10 such houses, you pay 1m$ out of your own pocket and you borrow the 9m$ at a rate of 3% (for simplicity assume an interest-only mortgage). What is your annual return? You make 500k in rental revenues. You pay back 270k in interest payments. Overall, you get 230k on an investment of 1m -> this gives you a return of 23%. Leverage allows you to increase your returns.

12. What if the value of all your houses drops by 10%? You still get 500k in rental revenues. You still have to pay 270k in interest payments. Now you make capital losses of 1000k. Your overall loss is 770k on an investment of 1m. -> Your return is -77%. Your returns are also amplified in the loss domain with higher leverage. 13. A bank invests 1m$, raises 9m$ of deposits and lends 10m$. Draw thebalance sheet of the bank. Assets Loans: 10m$

Liabilities Deposits: 9m$ Equity: 1m$

14. What is the leverage of the bank? Leverage is 10 to 1. 15. Now assume that the bank creates a special investment vehicle (SIV) and guarantees it. It sells 5m$ of its loans to the SIV. In exchange it receives 50k$ of equity and 4.95m$ in cash. The SIV holds 50k$ of capital and borrows the additional 4.95m$. Draw the balance sheet of the SIV. Assets Loans: 5m$

Liabilities Deposits: 4.95m$ Equity: 5k$

16. What is the leverage of the SIV? Leverage is 100 to 1. 17. What is the new balance sheet of the bank? Assets Loans: 5m$ Cash: 4.95m$ Stock in SIV: 50k

Liabilities Deposits: 9m$ Equity: 1m$

18 . Draw the consolidated balance sheet of the bank and the SIV. Assets Cash: 4.95 Loans: 10m$

Liabilities Deposits: 9m$ Debt: 4.95m$ Equity: 1m$

19 . What is the leverage of both the bank and the SIV? The true leverage of the bank is 14.95 to 1, which is higher than the apparent leverage of the bank (10 to 1). The creation of an SIV allows the bank to increase its leverage without the regulator noticing. 20 . What is a repo? A repurchase agreement is an overnight collateral loan.

21 What are the pros and the cons of financing with repos? Pro: Lower interest rate, it’s cheap Con: Need to roll-over the debt every day. In case of a liquidity crisis, you become shut down from credit markets. Ideology: That markets can self-regulate. Regulators underestimated the true leverage of financial institutions, who were using tricks (SIVs…). Beliefs that fundamentals were good -

Interest rates were historically low Low default rates in recent history

They had a separate political agenda of favoring home ownership of the poor. Regulator did not understand the risks that financial institutions were taking -

Some of these products were new and unknown to them These products were complex

22 Give some justifications for why regulators were believed to be too passive prior to the crisis. They believed in ever-increasing house prices – because they extrapolated recent trend in house prices. 23 What is the shadow banking sector? The shadow banking sector consists in all the financial institutions that do not fall under the regulatory framework of commercial banks. Examples include hedge funds, insurance companies, SIVs, government-sponsored agencies….. 24 What is the difference between standardized and customized derivatives? Customized derivatives are traded over the counter while standardized derivatives are traded on exchanges. Customized derivatives have more counterparty risk, they are less safer, they are less transparent, they are more difficult to compare to each other and they are less liquid. 25 What is the efficient markets hypothesis? The idea that market prices react instantly to every bit of new information. 26 What is a CDS? Credit default swap. It is a contract that insures its buyer against the loss from the default of a particular bond. 27 What is a naked CDS? It is a CDS bought by someone who does not own the underlying bond.

28 You buy a one-year bond with a 1000$ principal and 10% interest rate. You believe that the bond might default and buy a CDS for 50$. What are your possible returns if you buy the CDS and if you do not buy it?

Default No default

Buy the CDS -1000 5% -50+1100 -1000 5% -50+1100

No CDS 0

-100%

1100

10%

When you buy the CDS, your returns are less volatile. 29 What would be the returns if you would buy the CDS without owning the underlying bond?

Default No default

Buy the naked CDS -50 2100% +1100 -50+0 -100%

No naked CDS 0

0%

0

0%

The naked CDS is creating risk. 30 What is a subprime mortgage? A mortgage to a borrow who is below a certain credit score. 31 What is a 2/28 ARM mortgage? 30-year mortgage with fixed rate for 2 years and an adjustable rate for 28 years. ARM = adjustable rate mortgage 32 Why would a lender issue a mortgage that is designed to default? This is reasonable if you believe that house prices are going to increase. At the time of foreclosure, the lender will get all his money back. 33 Why would investment banks have an interest in selling complex securities that they did not understand themselves? The more complex the security, the less competition because it becomes more difficult to compare them. The issuer can charge a higher markup as result. 34 What issues does having rating agencies paid by the people they rate raise? This leads to grade inflation because you try to please your customer by giving him higher grades. 35 Why could it be an issue to have competition among rating agencies? This leads to rating shopping as you favor the institution that gives you the highest grade.

36 A trader works for an investment bank and can invest 1000$ in proportion p in a bond that pays 20% for sure and in proportion 1-p in a stock that pays a 100% return with probability 10%, 0% otherwise. If the trader is paid a proportion 10% of his profit, how does his portfolio look like? (assume linear utility) Utility of the trader is: 10% x share that goes to the trader

[p x 1000 x 20% return on bond

+

(1-p) x 1000 x 10% x 100%] expected return on stock

His utility is increasing in p because the bond pays a higher expected return.  The trader only invests in the bond -> p = 1  The salary of the trader is 20. 37 What if he receives a base salary 100 complemented by a bonus that represents 10% of his earnings if his return is above 20%? The utility of the trader becomes: 100 + base salary +

p x 1000 x (20% -20%) x bond return

10%

share that goes to trader

he only gets a share of the profit that exceed 20%

(1-p) x 1000 x 10% x (100% - 20%) x 10%

His utility is now decreasing in p, and so he only invests in stock. With bonuses, the trader maximizes his own payoff by maximizing the amount of risk that he takes (even though the stock has a lower expected return than the bond).

TUTORIAL 3 – ECONOMICS OF CRISES Baptiste Massenot 1. Give two reasons why mortgage related risk was higher than initially thought when the housing bubble burst. -

-

Investors believed mortgages were geographically diversified whereas they were concentrated in a few areas. Furthermore, geographical dispersion did not contribute to risk diversification because the housing bust affected all regions at the same time (correlated risk). Investors underestimated the leverage of financial institutions. Investors believed that ownership of mortgage related securities was much more dispersed whereas most of them were held by the big investment banks.

2. Why is a fall in asset value more likely to generate a market panic in case of high leverage? A fall in asset value means that the institution might become bankrupt (equity is wiped out). Higher leverage implies that it takes a lower drop in value to lead to default. 3. What is the typical tradeoff faced by a central bank? The central bank faces a tradeoff between growth/employment and inflation. Lower interest rates stimulate demand and thus increase both price and growth/employment. 4. In central banking, what is the difference between a dove and a hawk? A dove favors employment and a hawk favors stable inflation. 5. What factors can lead banks to face a liquidity crisis? Investors start doubting about the asset value of a bank (increased counterparty risk) and then stop lending to this bank (liquidity crisis). 6. According to Bagehot, what should central banks do in a liquidity crisis? Central banks should lend freely to these banks (as long as they are illiquid and not insolvent) against good collateral at a penalty rate), 7. What is the main benefit of the lender of last resort function of central banks? This prevent bank runs, liquidity crises. This prevents solvent banks from going bankrupt. 8. What was the main idea of the Term Securities Lending Facility? Increased counterparty risk implies that Treasuries are perceived to be to be the only safe securities left, so they are in high demand. The Fed has a lot of them and could thus swap them against the riskier securities held by banks. This provided liquidity to banks without expanding the balance sheet of the central bank and its associated higher money supply and inflation. 9. What were the three common characteristics of almost all financial institutions that failed during the recent crisis? They were all highly leveraged, they relied heavily on short-term debt, they were highly exposed to the mortgage-related markets.

10. Explain how fire sales can make an illiquid institution insolvent. If a financial institution has to urgently liquidate its assets, if might have to sell them at a lower price (fire sale price). This affect can be even stronger if many institutions sell the same type of assets at the same time. The resulting lower asset value can make the illiquid institution insolvent. 11. What is the basic tradeoff faced by regulators when the decision to save a financial institution comes? A bailout may lead investors to believe that all financial institutions will be saved in the future. So they might be less careful when lending to them -> higher risk-taking (moral hazard). The cost of no bailout is the possibility of a financial collapse/contagion to other institutions/markets. 12. How does the problem of moral hazard apply to financial institutions? When a government bails out a financial institution, markets expect that all other financial institutions will also be bailed out. This leads creditors to lend to riskier institutions. -> This increases the cost for the government because bailouts become more likely. 13. How was Bear Stearns saved? The Fed bought the riskiest assets of Bear Stearns to facilitate the merger with the commercial bank JP Morgan. 14. What distinguishes Fannie and Freddie from other financial institutions? They had an implicit guarantee from the government that allowed them to borrow more cheaply. This contributed to increase their leverage. They were not allowed to diversify into non-mortgage markets. These factors contributed to leave them more exposed to a decline in house prices. 15. Why was Bear Stearns bailed out and Lehman Brothers was not? Regulators received bad publicity from saving Bear, less available public money after saving Freddie and Fannie, assets were not as good (the company was more on the side of insolvency than illiquidity), fewer interested buyers (Barclays was interested but the deal was complicated because of legal and political reasons linked to an international merger), regulators believed that markets were now ready for a bank failure.

TUTORIAL 4 – ECONOMICS OF CRISES Baptiste Massenot 1. What is the main business of AIG? Selling insurance policies. 2. Give 2 reasons why AIG was seen as credible in selling credit default swaps. They had an AAA rating. As an insurance company, they sounded more creditable because of high equity. As an insurance company, they were less regulated and could hold less capital. 3. Give 2 reasons why AIG faced a liquidity crisis after the failure of Lehman. It had a large exposure to the CDS market and did not set aside enough capital. 4...