Financial Markets
GEORGE MASON UNIVERSITY
School of Management
EMBA 703 Financial Markets Dr. Hanweck
Final Examination
Fall 2013
NAME: ___________________________________Â G-code: _____________________________
Answer all questions. Place your answer to each question on a separate sheet of paper. Please write your name on the top left corner of each page. Document your answers and show your work. Read each question carefully and answer all parts. Try and answer something on each question. Your guess may turn out to be correct. The number in parentheses is the point weight for the question. Attach the exam to your answers.
(15) 1.(a) Discuss various measures of capital market efficiency and how efficient capital markets contribute to the efficiency in the market for goods and services (including productive capital). As part of your discussion, consider the implications of the fact that the bulk of trading in capital markets is in outstanding securities and analyze the meaning of the terms “depth,” “breadth,” and “resiliency” as descriptions of capital markets. Include in your discussion the types of legislative and regulatory reforms that might be or have recently been instituted in order to improve the efficiency of capital markets and the role of “insider trading” and the SEC as they affect market efficiency.
(b) Compare money and capital markets and identify the major issuers of securities in the different markets and the difference among the various types of securities within and between each of the markets. Within your discussion of the money markets include a consideration of the role of the Federal Reserve System (Fed) and the banking system as they interact through required reserve maintenance, needs for liquidity and monetary policy actions by the Fed. Consider in your analysis the types and significance of the links between the money and capital markets via the term structure of interest rates, issuers of debt and equity and the presence of interest rate and credit risk derivatives.
(10) 2. There are a number of theories of the term structure of interest rates including the unbiased expectations hypothesis, preferred habitat hypothesis, and market segmentation hypothesis. Discuss the implications of the unbiased expectations hypothesis within the context of the following problem. Problem 1: For a two year, default free, zero coupon security, compute its yield to maturity and draw the respective yield curves assuming two different expectations of inflation employing the Fisher Effect and the data below: (a) 4 percent one year from now, and (b) 2 percent one year from now. In addition, define and compute the implied forward yield on a one year security one year from now, assuming the current two year yield is 6.0 percent. Discuss the assumptions underlying this calculation and how it can be used to evaluate the implied forward yield on a 1-year loan, next year. (c) What is the implied expected rate of inflation if the real rate remains at 3 percent?
Use the following definitions and values:
R = 0.03 (constant real rate of interest)
p1 = 0.02 (period 1 rate of inflation)
(a) p2e = 0.04 (expected period 2 rate of inflation)
(b) p2e = 0.02 (expected period 2 rate of inflation)
1y1 = current yield on one year securities
2y1e = Expected period 2 yield on one year securities
1y2 = current yield to maturity on two year securities
Unbiased Expectations Hypothesis
In general, (1 + 1ym) = [(1 + 1y1)(1 + 2y1e). . .(1 + my1e)]1/m and jy1e = the forward rate, jf1.
Fisher Relationship: (1 + jy1) = (1 + jR1)(1+ jp1e ), where jp1e is the expected rate of inflation for period j for 1 year, and jR1 is the real rate of interest for period j for 1 year.
Specifically, (1 + 1y2) = [(1 + 1y1)(1 + 2y1e)]1/2 and 2y1e = the forward rate, 2f1.
The expected future 1-year yield factor is:
Don’t forget to draw the yield curves under assumptions (a) and (b), above, for each of the expected rates of inflation. Give the reasons for the shapes of these yield curves (HINT: are forward rates on future short-term securities equal to, greater than, or less than current short-term interest rates).
(15) 3. Mortgage markets have developed significantly since the early 1970s through the creation of secondary market instruments in the form of mortgage pass-throughs, collateralized mortgage obligations (CMOs), and REMICs. These collectively have been generally referred to as mortgage backed securities (MBS). In many ways, these instruments carry the characteristics of their underlying assets — individual mortgages. a. Why is the cash flow of a mortgage, or a MBS, uncertain in the sense that the investor in the mortgage has granted the borrower a call option to prepay the mortgage? Compare a mortgage cash flow with a Treasury coupon bearing bond paying interest semi-annually and a payment of principal at maturity. b. What does this call option depend upon and why? c. The cash flow for a mortgage pass-through typically is based on some prepayment speed benchmark. Why is the assumed prepayment speed necessary to price the MBS? d. Suppose a bank has decided to invest in a MBS and is considering the following two securities: a Freddie Mac pass-through with a WAM of 340 months and an average life of 7 years or a PAC tranche of a Freddie Mac CMO issue with an average life of 2 years. In terms of prepayment risk, contraction risk and extension risk, which MBS would probably be best for the bank’s asset/liability management perspective when it is known that liabilities generally have a duration less than 1 year and that assets have durations in the 2-year to 7-year range?
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Average life is:
e. Compare the interest rate risk of a noncallable 10-year Treasury coupon bearing bond with a mortgage-backed pass-through security with prepayments related to the level of interest rates – lower market interest rates raise the rate of prepayments. Discuss how the changes in cash flows from a mortgage-backed security affect the duration of such securities. HINT: consider the coupon effect on duration.
Macaulay Duration Measure:
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Pr
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A more complete approximation to the proportional change in price of a bond with respect to a change in yield to maturity takes into account the convexity of the price-yield relationship for the bond:
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dy
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where P = Price, C = coupon, F = Face value, y = Yield to maturity, M = maturity (years), t = time (year), dP is the total change in price, and

P
y
is the partial change in price with respect to a change in yield to maturity. The second term, excluding the dy2, is the convexity effect.
(10) 4. Are the following statements consistent or inconsistent? Explain your answer and discuss how equilibrium is achieved between the futures and cash markets.
1. Futures markets serve an important function of the global financial markets by giving investors the opportunity to better manage financial risks associated with their underlying business transactions.
2. The futures market is where price discovery takes place.
3. The introduction of futures contracts creates greater price volatility for the underlying commodity or financial asset.
(10) 5. Suppose the current yields to maturity on 3‑month and 6‑month T-Bills are 4.0 percent and 5.0 percent, respectively (yields will need to be converted to 90-day returns).
(a) In perfectly efficient markets and risk-neutral pricing, what yield should you expect to find on a 3‑month T-bill forward contract deliverable in 3 months?
(b) Show that for the forward yield calculated in (a) the 6‑month returns on (i) a 6‑month spot bill and (ii) 3‑month spot and 3‑month futures bills are the same.
(c) Explain what factors would lead to a rejection of (b).
NOTE: From the term structure of interest rates recall:
(1 + oy2)2 = (1 + oy1)(1 + 1F1)
where oy2 = the cash 6‑month bill (two‑period) yield,
oy1 = the cash 3‑month bill (one‑period) yield,
1F1 = the 3‑month (one‑period) forward yield one period from now.
ALSO, in the futures market:
(1 + oy2)2 = (1 + oy1)(1 + 1y1f),
where 1y1f = the 3‑month futures yield on futures contracts due in three months.
(15) 6. Consider the following bank balance sheet (fixed rates and pure discount securities unless indicated otherwise). Interest rates on liabilities (yL) are 3 percent and on assets (yA) are 6 percent.
Duration
($millions) (years)
Super Now Checking Accounts (rates set daily) $150 1.5
6‑Month Certificates of Deposit 50 .5
3‑Year Certificates of Deposit 35 3.0
Total Liabilities 235 ?
Net Worth 20Â –
Total Liabilities and Net Worth 255 ‑
Prime‑Rate Loans (rates set daily) 75 1.0
2‑Year Car Loans 100 1.5
30‑Year Mortgages 80 7.0
Total Assets 255 ?
a. Find the duration of assets and liabilities.
b. Will the bank benefit or be hurt if all interest rates rise? Bank management can protect itself by (buying)/(selling) Treasury bond futures contracts. Explain by considering basis risk using interest rate futures to hedge a position with a variety of assets. How can the duration gap be managed through the use of financial futures contracts based on 10-year Treasury bonds? Define your terms and state clearly your assumptions.
c. Which asset is causing the substantial duration mismatch? Since the bank would take a capital loss if interest rates rose, what type of interest rate options contract would help hedge this possibility – buy a cap, sell a cap, buy a floor or sell a floor or some combination?
d. 2-year car loans and prime rate loans are subject to greater default risk as interest rates rise, how might the bank use a credit default swap applied to each loan and for what notional values? Are the collateralized loans (2-year car loans) or the uncollateralized prime rate loans more default risky if the likelihood of default within one year is 0.02 for each and why?
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ï„E = change in the market value of equity,
DA = duration of assets,
DL = duration of liabilities,
L = market value of liabilities,
A = market value of assets, and
ï„y = change in interest rates.
(15) 7.(a) Within the loanable funds theory, graphically show the effect of an increase in the money supply, assumed to be determined solely by the Fed, on the supply and demand for loanable funds and the equilibrium rate of interest assuming a constant real rate of interest and expected inflation to be constant.
(b) Illustrate and discuss how an autonomous increase in the expected rate of inflation will change the equilibrium nominal interest rate. Consider an initial real rate of interest of 3 percent and an expected inflation rate of 2 percent. If the expected rate of inflation rises to 4 percent with the real interest rate constant, what would the resulting nominal interest rate become, using the Fisher relationship? The rise in the expected rate of inflation is considered to remain at the higher level. Define your terms and discuss a recommended monetary policy to achieve economic stabilization with price stability and an improvement in the balance of payments.
(c) Starting from an equilibrium position as in 7.a, discuss the effects of the conduct of a more restrictive monetary policy if the markets believe that a Fed tightening will lower future (next period) inflation. How might a recession occur under this scenario?
HINTS: Recall the Fisher relationship where (1+i) = (1+r)(1+pe), where i is the nominal interest rate, r is the required real rate of return before taxes, and pe is the expected rate of inflation.
DLF = I + G – T + NX I = real investment; NX = net exports
G – T = the government deficit (excess of government spending over tax revenues).
SLF = S + ï„Ms – H S = private savings H = desired hoarding
ï„Ms = change in the money supply (under Federal Reserve discretionary control).
D
LF
LF
0
i*
Q*
LF
Loanable Funds ($)
Interest
Rate (%)
(10) 8. As a financial institutions and market analyst for WatchYourBack.Com Securities, Inc., a highly reputable financial institutions’ securities underwriter and Internet broker, you must prepare an analysis of the financial condition of a broad range of financial institutions of various sizes, localities, and product lines. Using the “probability of insolvency” model discussed in class where E(ROA) is the expected annual value of after tax earnings on assets over the next 2 years, ï³2is the expected annual variance of ROA over the next 2 years, and K/A is the firm’s current Tier I Capital, K, to total assets, A: (a) discuss, based upon your assumptions concerning the risk-return tradeoff embodied in the efficient frontier of possible FI portfolios, what factors determine each of these parameters of financial soundness over the next few years. (b) In addition, discuss how the federal regulatory capital adequacy policy, in the form of risk based capital adequacy standards and Prompt Corrective Action (and as proposed in Basel III and the Volcker Rule), might affect bank and thrift soundness and depository institutions’ portfolio choices by comparing points A and B below and different choices of capitalization as revealed in the FI’s choice of K/A. In this discussion, how does the “too-big-to-fail” policy affect the bank’s choice of risk and return and willingness to take risks? Are moral hazard costs increased under a liberal “too-big-to-fail” policy and have the expanded powers of FIs following the passage of the Gramm-Leach-Blily Act increased or decreased these costs?
(c) Which bank portfolio, A with [K/A]0 or B with [K/A]1, has the greater maximum likelihood of insolvency and why? From this conclusion, which bank portfolio could sustain a greater loss of capital value at a 5 percent confidence level assuming ROA is distributed as a normal variable with mean E(ROA) and variance ï³2?
NOTE: maximum probability of insolvency = ï³2/[E(ROA) + K/A]2 (as derived from Chebychev’s Inequality Theorem). Insolvency means falling below a portfolio valuation of zero.
0
ROA
s
Risk
E(ROA)
A
-[K/A]
B
Efficient Frontier
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ROA
/ (Probability of Insolvency)
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