Econ215 Chapter 3

Econ215 Chapter 3 - Part 2 Market Fundamentals Overview...

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Part 2 Market Fundamentals

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Overview There are two main approaches to evaluating securities: Fundamental Analysis Technical Analysis
Chapter 3 Time Value of Money

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Question : How much is a future sum of money worth now? Suppose time is measured in equally spaced intervals as t = 0, 1, 2, 3, … Let X t denote a cash flow received in time period t. Rephrased Question : How much should an investor pay now for a contract that delivers X t at time t?
Assumptions The interest rate i is constant across time. There is no uncertainty concerning the future. The same bank interest rate prevails for borrowing and lending.

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Opportunity Cost : The cost incurred by the loss of potential gains from other alternatives when one action is taken. Example: Compare stuffing a dollar into a mattress for T time periods versus depositing it in a savings account and drawing compound interest.
Mattress Stuffing Strategy: The investor ends up with the amount Y after T periods. Savings Account Strategy: The investor ends up with the amount Y(1+i) T after T periods.

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Application Suppose two agents are contemplating exchanging a contract for an amount Y. From the viewpoint of the buyer, Y is the present cost and X t is the future benefit. From the viewpoint of the seller, Y is the present benefit and X t is the future cost.
Buyer’s Viewpoint An alternative opportunity is to deposit the amount Y in a savings account that draws compound interest. Let i = the inter-period interest rate paid by the bank After t time periods, the savings Y has compounded into the amount Y(1+i) t

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Seller’s Viewpoint An alternative opportunity is to borrow the amount Y from a bank and roll over the debt. Let i = the inter-period interest rate charged by the bank After t time periods, the debt Y has compounded into the amount Y(1+i) t
There are three possibilities: Case (1): X t < Y(1+i) t Case (2): X t > Y(1+i) t Case (3): X t = Y(1+i) t

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Case (1) o Suppose X t < Y(1+i) t . Then the potential buyer of the contract receives greater future benefit from investing the amount Y into a savings account now and withdrawing it at date t. o Thus, a rational investor would buy the contract only if X t > Y(1+i) t .
Case (2) o Suppose X t > Y(1+i) t . Then the potential seller of the contract incurs a smaller future cost by borrowing the amount Y from the bank and rolling over the debt until date t. o Thus, a rational investor would sell the contract only if X t < Y(1+i) t .

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Case (3) o Suppose X t = Y(1+i) t . This is the only case in which two rational agents would agree to exchange the contract for the amount Y. o Alternatively, Y = X t /(1+i) t is the market price of the contract.
Now versus the Future Future Value Y(1+i) t X t Present Value Y X t /(1+i) t The quantity Y(1+i) t is the future value of Y.

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