EC3333 Financial Economics I

1

Wong Wei Kang

Outline

Module Info Topics Covered Real Assets vs. Financial Assets The Role of Financial Markets Effective Annual Rate (EAR) Annual Percentage Rate (APR) Nominal vs. Real Returns

2

Contact Information Instructor: Wong Wei Kang Office: AS2-04-20 Email: coswong@nus.edu.sg Dont email me your questions Post your questions to IVLE Discussion Forum

Facebook: https://www.facebook.com/wongweikang

Class Group on Facebook: https://www.facebook.com/groups/239061682957919/ or search EC3333 Sem 1, 2014-2015

3

IVLE Syllabus Lecture Notes Tutorial Questions No assignment; No submission Attempt before class; Participate in discussion

Discussion Forum Dont email me your questions Post your questions to IVLE discussion forum

4

References Main Textbooks Zvi Bodie, Alex Kane, Alan J. Marcus, Ravin Jain

(2014), Investments, McGraw-Hill. Older versions OK. Its up to you

Supplementary Textbook Berk and DeMarzo, Corporate Finance, 3e Two very enthusiastic thumbs up for this textbook Its clearly written, coherent, exciting and

insightful.

5

Assessment

Tutorial Attendance and Participation: 15% Midterm Exam: 35% (Closed Book) Final Exam: 50% (Closed Book)

Format of Exam will be discussed in lecture

later We will not use a financial calculator

6

Excelling in the Course

1. Attend lecture 2. Read & understand lecture notes 3. Read & understand textbooks 4. Attempt the tutorial questions before class 5. Attend tutorial & participate in discussion 6. Clarify doubts immediately

7

Topics Portfolio theory Capital Asset Pricing Model (CAPM) Arbitrage Pricing Theory (APT) Valuation Models of Financial Assets Equity: Stocks (maybe, maybe not) Fixed-Income Securities: Bonds Derivative Securities: Options, Forward and

Futures Contracts

8

Definitions of Assets An asset is any possession that has value in an

exchange. Real Assets (focus of Macroeconomics)

Determine the productive capacity of the economy Land, buildings, machines, knowledge used to produce

goods and services

Financial Assets (focus of Financial Economics) Claims to incomes generated by real assets or from

the government Fixed incomes or debts: Bonds Stock or equity Derivative securities

9

Financial Markets and the Economy The Information Role of Financial Markets Stock prices reflect prospects of the companies Transfer of capitals from investors to companies

Consumption Timing Save now and spend in the future or vice versa

Allocation of Risk Investors have different risk preference

Separation of management and ownership But potential principal-agent problem as managers,

hired as agents of the shareholders, may pursue their own interests instead of maximizing firm value

10

Effective Annual Rate (EAR)

11

Indicates the total amount of interest that will be earned at the end of one year

Considers the effect of compounding a.k.a. the effective annual yield (EAY) or annual

percentage yield (APY) For investments that last < 1 year, we compound

the per-period return for a full year EAR = ( 1+ rate for period)Number of periods per year 1

Effective Annual Rate (EAR)

12

Because of compounding, earning a 5% return annually is not the same as earning 2.5% every six months.

Suppose one is earning 2.5% every 6 months 1+EAR = (1+0.025)2 = 1.0506 EAR = 0.0506 = 5.06%

Earning 2.5% every six months = earning 5.0525% a year It is greater than 5% because you earn interest on interest

Suppose one is earning EAR=5%, it is approximately the same as earning 2.47% every six month. (1+r)2 = 1.05, where r = interest rate for six months r = (1.05)1/2 1= 1.0247 1 = .0247 = 2.47%

Annual Percentage Rate (APR)

13

The annual percentage rate (APR), indicates the amount of simple interest earned in one year.

Simple interest is the amount of interest earned without the effect of compounding.

The APR is typically less than the EAR. Rates on investments that last < 1 year are often

annualized using simple rather than compound interest

Annual Percentage Rate (APR) The APR itself cannot be used as a discount rate.

The APR with k compounding periods per year is a way of quoting the actual interest earned each compounding period

Suppose a bank advertises savings accounts with an interest rate of 6% APR with monthly compounding. In this case, you will earn 6%/12=0.5% every month. Because the interest rate compounds each month, you will earn

(1.005)12 = 1.061678 at the end of one year, for an EAR of 6.1678%

In later months, you earn interest on the interest paid in earlier months

APRInterest Rate per Compounding Period periods / year

=k

Converting APR to EAR

The EAR increases with the frequency of compounding. As the compounding frequency grows and the

compounding interval gets smaller, in the limit we get continuous compounding (CC)

Continuous compounding is compounding every instant. rcc = APR for the continuously compounded case

1 1 + = +

kAPREARk

1 exp( ) CCrCCEAR r e+ = =

ln 1+ EAR( ) = rCC

Converting APR to EAR

A 6% APR with continuous compounding results in an EAR of approximately 6.1837%.

Table 5.1B Effective Annual Rates for a 6% APR with Different Compounding Periods

Real and Nominal Rates of Interest Real: the growth rate of purchasing power, r Nominal: the growth rate of money, i Inflation rate: the growth rate of prices,

How are the real/nominal interest rates decided in theory and in practice?

17

1+ r = 1+ i1+

1+ r + + r =1+ i

r = i 1+

or r i

Equilibrium Interest Rates Equilibrium real interest rate

loanable funds market, where the demand for loanable funds equals supply

Equilibrium nominal interest rate As the inflation rate increases, investors will demand

higher nominal rates of return If e denotes current expectations of inflation, then we

get the Fisher Equation: Nominal rate = real rate + inflation forecast

Fisher Effect: The one-for-one relation between the inflation rate and the nominal interest rate

i = r + e

Figure 5.1B U.S. Nominal Interest Rates & Inflation Rates, 19602012 (Correlation is about 0.77)

Moderate inflation can offset most of the nominal gains on low-risk investments

A dollar invested in T-bills from 19262012 grew to $20.25 but with a real value of only $1.55

Persistent negative correlation between real rate and inflation rate means the nominal rate doesnt fully compensate investors for increased in inflation The nominal interest rate has tended to respond less than

one-for-one to changes in expected inflation

Bills and Inflation, 1926-2012

The correlation of inflation with both nominal and real T-bills

Figure 5.2 Nominal and real wealth indexes for investments in Treasury bills, 19682009 (inset figure is for 19262009)

Figure 5.3 Nominal Interest Rates on T-bills and Inflation, 1926-2012

References

BKM, Sections 1.1-1.3, Sections 5.1-5.3. BD, Section 5.1, Section 5.3.

23