Note-2 - Risk & Return

Note-2 - Risk & Return - Economics 106V Investments:...

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Economics 106V Investments : Lecture Note-2 Daisuke Miyakawa UCLA Department of Economics June 27, 2008 2nd lecture covers the following items: (1) The determinants of return, (2) various measurements of risk and return, (3) the concepts of Mean-Variance Criteria and Sharpe ratio, and (4) the demonstration of the concepts. After discussing those items, we solve some exercise problems. 1 The Determinants of Return 1.1 Demand and Supply Same as a usual goods market, supply and demand determine the price of money (i.e., "return" or "interest rate"). In this money market, households are the main suppliers of the money through its saving while business sector mainly demands (i.e., wants to borrow) the fund. Note that government in general acts as a supply side and a demand sides through Federal Reserve Actions. Figure-1 summarizes the determination of the interest rate through the supply and demand. Figure-1: Demand and Supply of Funds 1.2 Fisher Equation As you studied in the introductory macroeconomics course, we have a key equation called as Fisher equation, which describes the relationship between real and nominal interest rates. The equation is as follows: 1 + R = (1 + r ) (1 + i ) , 1+ R 1+ i = 1 + r where R : Nominal interest rate r : Real interest rate i : 1
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Note that investors care about the real rate rather than the nominal one (why?). By using the equation, you can compare several di/erent situations. For example, as an investor (i.e., buy some bonds or lend some money) which of the situations is more preferable? On this course, we mainly focus on the real interest rate (i.e., ignore the in±ation e/ect). 2 Various Measurements of Risk and Return 2.1 Return 2.1.1 Return and Price of Zero-Coupon Bond First, we discuss the relationship between the future price of a "zero-coupon bond" sold at $100 today and its return over a certain period. r f ( T ) = P ( T ) 100 1 where r f ( T ) : The return from the T-period investment P ( T ) : The price of the bond at T-period from now 2.1.2 Two Methods to Annualize the Return How can we annualize the return? There are two major methods to do this. E/ective Annual Rates First method is to annualize the life-time return by using a compound interest rate. This is a theoretically correct way to annualize. EAR = f 1 + r f ( T ) g 1 T 1 Annualized Percentage Rates Second method is to annualize the life-time return by using a simple interest rate (i.e., not compound). This is conventionally used in advertisement and not necessarily correct in a theoretical sense as we see below. APR
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This note was uploaded on 09/23/2008 for the course ECON 106v taught by Professor Miyakawa during the Summer '08 term at UCLA.

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Note-2 - Risk & Return - Economics 106V Investments:...

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