Please start working in the following problems right a way.

note: if clarification needed please let me know.

We have some basic principles (or basic theories) of finance. They are 'time value of money, risk return trade off, valuation, leverage, bond prices vs. interest rates, liquidity vs. profitability, matching principle (or principle of suitability), portfolio (diversification) effect, and absence of arbitrage. Absence of arbitrage is required for market equilibrium. It suggests that no extra profit without investment can be obtained in a market in equilibrium. Now, explain the following terminologies. (1) Time value of money (2) Risk return trade off (3) Portfolio (diversification) effect Discuss theory on risk preference in three categories taking investor's attitude toward risk. Also illustrate in utility curves. Consider a used car market in which differences in the care with which owners use their cars lead to quality differences among cars that started out identical. It is natural to suppose that the owner of the used car knows more about its quality than potential buyers. As an example, assume that there are three possible quality levels that the used car in question can have, q1 > q2 > q3 = 0. If the quality level is q3, the car is a lemon. Such a car would be priced as being worthless if buyers could correctly assess its quality. If the quality is q2, the car has a value of $5, and if the quality is q1, the car is worth $10. Assume that all agents are risk neutral and a buyer does not want to pay more for a car than its expected worth. In like vein, the car owner does not wish to sell at less than what the car is worth. Suppose that each car owner knows his car's quality, but buyers only know that cars for sale can be of quality q1, q2, or q3. Faced with a given car, they cannot identify its precise quality. However, they believe that there is a probability 0.4 that the quality is q1, a probability 0.2 that it is q2, and a probability 0.4 that it is q3. What will happen in such a market? Show it mathematically. See following table and answer the questions. Payoffs in State Securities Current Price R1 H $100 L 0 R2 0 $100 B $50 $50 $40 $40 $43 (1) Show how you could make arbitrage profit and how much? (2) Explain the way how the market attains equilibrium. Introduce key informational problems that make the role of F.I.s necessary. Introduce two information-based financial services provided by F.I.s. Consider an imaginary 'marriage market.' There are 100 men and 100 women searching for the \"perfect\" marriage partner. Let x = 100 (number of searchers) and c = $25 (cost of evaluating one person by meeting). Answer the following queations. (1) What is the total evaluation cost (without introduction of a marriage broker)? (2) Now, introduce a broker who needs to evaluate each man and woman only once. What will happen to the total evaluation cost? (3) Calculate the amount of savings by introduction of a marriage broker. (4) Show that the saving is increasing as the size of the grid expands. -1- Show the need for central-bank-based lender-of-last-resort facility using goldsmith anecdote and the concept of fractional reserve banking system. Also suggest what problem will arise from it. [Moral hazard problem] Consider a firm that will liquidate one period hence at time t=1. Assume that there are no taxes and the firm can invest $60 in a risky venture at t=0 using retained earnings. If the investment is not made, shareholders get a dividend of $200 at t=0. The firm's debt requires a payment of $200 at t=1, and its investment choices are described in the table below. For simplicity, assume that the discount rate is zero. Payoffs related to different investment opportunities State of Nature Strategy Total firm value at t=1 if no investment made and $200 dividend paid at t=0 Total firm value at t=1 if $60 investment made and $140 dividend paid at t=0 Boom (with probability 0.5) Bust (with probability 0.5) $220 $140 $400 $ 10 Answer the following questions (1) Calculate the net present value (NPV) of each choice for the firm as a whole and say what your suggestion from your estimation. (2) Suppose that you are a manager working for the shareholders. You know that they want you to maximize their claim before considering the firm value as a whole. What then is your choice would be? Numerically show that why your choice as a manager is palatable to the shareholders. Also show how much the shareholders get (or lose) by making a decision that way? (3) What is the implication from the answer to question 2) above? (4) Estimate the expected payoff to the bondholders. (5) What will happen to the wealth of the bondholders if the shareholders invest in the risky project? (6) Calculate the aggregate loss due to moral hazard. So that there is a net decline in total firm value of $35 ($30-$65=-$35). (7) It is accepted that F.I.s' special skills in monitoring attenuate moral hazard. Illustrate the examples. It is shown that 'regulation is endogenous, the central bank is endogenous, and that fractional reserve banking is endogenous.' Briefly explain why? Deposit insurance is an alternative to the lender-of-last-resort facility is deposit insurance provided by the government. But, it shifts the burden of keeping the bank in check from the private market to the regulator. It is because private arrangements did not possess unlimited capacity. Then, what kind of counter-measures are needed? Show examples. Illustrate the macroeconomic implications of FCM (fixed coefficient model) by introducing major tools of monetary policy. Explain the following terminologies briefly. Insider debt vs. outside debt. Transaction vs. relationship loans. Answer the following questions. (1) Why are banks thought to be most able broker in financial markets? (2) QAT (qualitative asset transformation) is a very important way of bank's making money, where some forms of risks are taken or given up in exchange for profit. QAT is carried out by performing mismatches between assets and liabilities. Illustrate major the mismatches and risks that have to be taken by banks. You had better illustrate the relationship by an appropriate figure. -2- Answer the following quesrtions. (1) What is yield to maturity (YTM)? (2) What is term structure of interest rates (or the yield curve) (3) What is duration? We can find spot interest rates in the market. We, however, cannot tell what the future interest rate will be. Instead, we can estimate future forward rates using expectations hypothesis. Now, suppose the four year, three year, two year interest rate is 12%, 9%, and 7% each. Current one year market interest rate is 5%. Answer the following questions. (1) What is the one-year forward rate at the end of the first year ( (2) ). (3) What is the one-year forward rate at the end of the second year ( (4) ). (5) What is the one-year forward rate at the end of the third year ( (6) ). From the implication of duration and bank's equity value, we can derive the following implicational equation: / / (1) What drives the change in the bank's equity value when market yields change? (2) Show the condition under which the bank will be immunized. Suppose you have 10-year zero-coupon bond, risk free, par value of $1,000, priced to yield 10%. Answer the following questions. (1) Find current price (2) Estimate duration-predicted price given +500 b.p. yield change. (3) Estimate duration-predicted price given -500 b.p. yield change. (4) It is known that duration-predicted price is different from actual price. Why? -3