FIN 072 | Financial Markets

Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

Lesson Title: Materials:

Risk and Rates of Return (Part 1) Calculator, reviewer notebook,
Graded Quiz 1 textbook
Lesson Objectives:
At the end of this module, I should be able to: References:
1. Compare expected return with required and realized return; Timbang, F. (2016). Financial
2. Identify the types of risks; and Management Part 2. Quezon City: C
3. Discuss the concept of standard deviation. & E Publishing, Inc.

Brigham, E. F., Houston, J. F., Hsu, J.-

M., Kong, Y. K., & Bany-Ariffin, A.
(2018). Essentials of Financial
Management. Pasig City: Cengage
Learning Asia Pte. Ltd.

Productivity Tip:
Take Breaks
It is important to note that the most effective breaks are those where you get away from your study space and
take your mind off the task at hand. You are not really going to be resting your mind if you are still at your
desk and thinking about all the assignments you must do. Instead, walk around the house, take a short walk,
get something to eat, and just clear your mind as much as you can.

A. LESSON PREVIEW/REVIEW
1) Introduction (2 mins)
Welcome back! Let us review the lesson on the previous day.
Your grandmother just died and left you P100,000 in a trust fund that pays 6.5% interest. You must spend the
money on your college education, and you must withdraw the money in 4 equal installments, beginning
immediately. How much could you withdraw today and at the beginning of each of the next 3 years and end up
with zero in the account?
Solution:

Answer:

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

2) Activity 1: What I Know Chart, part 1 (3 mins)

What I Know Questions: What I Learned (Activity 4)

What are the determinants

of interest rates?

What is Pure Expectation

Theory?

B. MAIN LESSON
1) Activity 2: Content Notes (13 mins)
What four factors affect the level of interest rates?
• Production opportunities
• Time preferences for consumption
• Risk
• Expected inflation

“Nominal” vs. “Real” Rates

r = represents any nominal rate
r* = represents the “real” risk-free rate of interest. Like a T-bill rate, if there was no inflation. Typically
ranges from 1% to 4% per year.
rRF = represents the rate of interest on Treasury securities.

Determinants of Interest Rates

r = r* + IP + DRP + LP + MRP
r = required return on a debt security
r* = real risk-free rate of interest
IP = inflation premium
DRP = default risk premium
LP = liquidity premium
MRP = maturity risk premium

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

Premiums Added to r* for Different Types of Debt

Constructing the Yield Curve: Inflation

• Step 1: Find the average expected inflation rate over Years 1 to N:
N
 INFL t
t =1
IPN =
N
Assume inflation is expected to be 5% next year, 6% the following year, and 8% thereafter.
IP1 = 5% / 1 = 5.00%
IP10 = [5% + 6% + 8%(8)] / 10 = 7.50%
IP20 = [5% + 6% + 8%(18)] / 20 = 7.75%
Must earn these IPs to break even vs. inflation; these IPs would permit you to earn r* (before taxes).

Constructing the Yield Curve: Maturity Risk

• Step 2: Find the appropriate maturity risk premium (MRP). For this example, the following equation will
be used to find a security’s appropriate maturity risk premium.
MRPt = 0.1% (t – 1)
Using the given equation:
MRP1 = 0.1%  (1 − 1) = 0.0%
MRP10 = 0.1%  (10 − 1) = 0.9%
MRP20 = 0.1%  (20 − 1) = 1.9%
Notice that since the equation is linear, the maturity risk premium is increasing as the time to maturity
increases, as it should be.

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

Add the IPs and MRPs to r* to Find the Appropriate Nominal Rates
• Step 3: Adding the premiums to r*.
rRF, t = r* + IPt + MRPt
Assume r* = 3%,
rRF,1 = 3% + 5% + 0.0% = 8.0%
rRF,10 = 3% + 7.5% + 0.9% = 11.4%
rRF,20 = 3% + 7.75% + 1.9% = 12.65%

Hypothetical Yield Curve

• An upward-sloping yield curve.
• Upward slope due to an increase in expected inflation and increasing maturity risk premium.

Relationship Between Treasury Yield Curve and Yield Curves for Corporate Issues
• Corporate yield curves are higher than that of Treasury securities, though not necessarily parallel to the
Treasury curve.
• The spread between corporate and Treasury yield curves widens as the corporate bond rating
decreases.
• Since corporate yields include a default risk premium (DRP) and a liquidity premium (LP), the corporate
bond yield spread can be calculated as:
Corporate bond
= Corporate bond yield − Treasury bond yield
yield spread
= DRP + LP

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

Illustrating the Relationship Between Corporate and Treasury Yield Curves

Macroeconomic Factors That Influence Interest Rate Levels

• Federal reserve policy
• Federal budget deficits or surpluses
• International factors
• Level of business activity

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

2) Activity 3: Skill-building Activities (with answer key) (18 mins + 2 mins checking)
Activity 3.1. Compare expected return with required and realized return
Direction: Define the following. (3 minutes)
1. Risk - ______________________________________________________________________________________________________
2. Expected Return - _________________________________________________________________________________________
3. Required Return - _________________________________________________________________________________________
4. Realized Return - __________________________________________________________________________________________

Activity 3.2. Identify the types of risks

Direction: Write SR if the risk is a Systematic Risk. Write UR if the risk is an Unsystematic Risk. (5 minutes)
1. ____________ - Interest Rate Risk
2. ____________ - Purchasing Power Risk
3. ____________ - Event Risk
4. ____________ - Principal Risk
5. ____________ - Currency Risk
6. ____________ - Credit Risk
7. ____________ - Equity Risk
8. ____________ - Liquidity Risk
9. ____________ - Inflation Risk
10. ____________ - Call Risk
11. ____________ - Country Risk
12. ____________ - Business Risk

Activity 3.3. Discuss the concept of standard deviation

Direction: Solve the problems. (20 minutes)
Activity 3.3.a. Using the 5-year annualized total returns for five investment managers if the managers'
individual returns were 30%, 12%, 25%, 20%, and 23%, answer the following questions:
1. Population variance = _________________
2. Population standard deviation = _________________
3. Sample variance = _________________
4. Sample standard deviation = _________________

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

1. Solution: 2. Solution:

3. Solution: 4. Solution:

Activity 3.3.b. Assume that Conrado Corporation is considering the possible rates of return it might earn
next year on a P100,000 investment on the stocks of Buenos Aires or a P75,000 on those of Jessa. The
future returns depend on the state of the economy with their corresponding probability distribution.
Stock Buenos Aires Stock Jessa
State of Economy Return (r) Probability (p) Return (r) Probability (p)
Bad -8% 15% -10% 20%
Normal 15% 70% 20% 80%
Good 35% 15% 40% 20%
1. What is the Expected Return of Stock Buenos Aires? ___________________
2. What is the Expected Return of Stock Jessa? ___________________
3. What is the Variance of Stock Buenos Aires? ___________________
4. What is the Variance of Stock Jessa? ___________________
5. What is the Standard Deviation of Stock Buenos Aires? ___________________
6. What is the Standard Deviation of Stock Jessa? ___________________
7. What is the Coefficient of Variation of Stock Buenos Aires? ___________________
8. What is the Coefficient of Variation of Stock Jessa? ___________________

State of the r p rp (r-mean) (r-mean)^2 [(r-mean)^2]

Economy (p)
Bad -8% 15%
Normal 15% 70%
Good 35% 15%
Total

State of the r p rp (r-mean) (r-mean)^2 [(r-mean)^2]

Economy (p)

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

Bad -10% 20%

Normal 20% 80%
Good 40% 20%
Total

3) Activity 4: What I Know Chart, part 2 (2 mins)

4) Activity 5: Check for Understanding (5 mins)

Graded Quiz 1
Write your final answers here: Score:
1 6 11
2 7 12
3 8 13
4 9 14
5 10 15

Part 1. Modified True or False. Write:

A – Both statements are true
B – Both statements are false
C – Only statement A is true
D – Only statement B is true
1 A If you decide to buy 100 shares of Google, you would probably do so by calling your broker and
asking him or her to execute the trade for you. This would be defined as a secondary market
transaction, not a primary market transaction.
B The term IPO stands for "individual purchase order," as when an individual (as opposed to an
institution) places an order to buy a stock.
2 A In a "Dutch auction" for new stock, individual investors place bids for shares directly. Each potential
bidder indicates the price he or she is willing to pay and how many shares he or she will purchase
at that price. The highest price that permits the company to sell all the shares it wants to sell is
determined, and this is the "market clearing price." All bidders who specified this price or higher
can purchase their shares at the market clearing price.
B When a corporation's shares are owned by a few individuals who are associated with the firm's
management, we say that the stock is closely held.
3 A A publicly owned corporation is a company whose shares are held by the investing public, which
may include other corporations as well as institutional investors.
B If you wanted to know what rate of return stocks have provided in the past, you could examine
data on the Dow Jones Industrial Index, the S&P 500 Index, or the NASDAQ Index.

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

4 A The annual rate of return on any given stock can be found as the stock's dividend for the year plus
the change in the stock's price during the year, divided by its beginning-of-year price.
B As a result of compounding, the effective annual rate on a bank deposit (or a loan) is always equal
to or greater than the nominal rate on the deposit (or loan).
5 A Midway through the life of an amortized loan, the percentage of the payment that represents
interest must be equal to the percentage that represents repayment of principal. This is true
regardless of the original life of the loan or the interest rate on the loan.
B The payment made each period on an amortized loan is constant, and it consists of some interest
and some principal. The closer we are to the end of the loan's life, the smaller the percentage of
the payment that will be a repayment of principal.

Part 2. Problem Solving. Provide the required information.

6 You are considering investing in a bank account that pays a nominal annual rate of 7%, compounded
monthly. If you invest P3,000 at the end of each month, how many months will it take for your account
to grow to P150,000?
7 Your child's orthodontist offers you two alternative payment plans. The first plan requires a P4,000
immediate up-front payment. The second plan requires you to make monthly payments of P137.41,
payable at the end of each month for 3 years. What nominal annual interest rate is built into the monthly
payment plan?
8 You just deposited P2,500 in a bank account that pays a 4.0% nominal interest rate, compounded
quarterly. If you also add another P5,000 to the account one year (4 quarters) from now and another
P7,500 to the account two years (8 quarters) from now, how much will be in the account three years (12
quarters) from now?
9 Suppose you borrowed P15,000 at a rate of 8.5% and must repay it in 5 equal installments at the end of
each of the next 5 years. By how much would you reduce the amount you owe in the first year?
10 Your brother's business obtained a 30-year amortized mortgage loan for P250,000 at a nominal annual
rate of 7.0%, with 360 end-of-month payments. The firm can deduct the interest paid for tax purposes.
What will the interest tax deduction be for Year 1?
11 Suppose the real risk-free rate is 4.20%, the average expected future inflation rate is 3.10%, and a maturity
risk premium of 0.10% per year to maturity applies, i.e., MRP = 0.10%(t), where t is the number of years
to maturity, hence the pure expectations theory is NOT valid. What rate of return would you expect on a
4-year Treasury security? Disregard cross-product terms, i.e., if averaging is required, use the arithmetic
average.
12 Suppose the yield on a 10-year T-bond is currently 5.05% and that on a 10-year Treasury Inflation
Protected Security (TIPS) is 2.15%. Suppose further that the MRP on a 10-year T-bond is 0.90%, that no
MRP is required on a TIPS, and that no liquidity premium is required on any T-bond. Given this

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

information, what is the expected rate of inflation over the next 10 years? Disregard cross-product terms,
i.e., if averaging is required, use the arithmetic average.
13 Koy Corporation's 5-year bonds yield 7.00%, and 5-year T-bonds yield 5.15%. The real risk-free rate is r*
= 3.0%, the inflation premium for 5-year bonds is IP = 1.75%, the liquidity premium for Koy's bonds is
LP = 0.75% versus zero for T-bonds, and the maturity risk premium for all bonds is found with the formula
MRP = (t − 1) × 0.1%, where t = number of years to maturity. What is the default risk premium (DRP) on
Koy's bonds?
14 Niendorf Corporation's 5-year bonds yield 8.00%, and 5-year T-bonds yield 4.80%. The real risk-free rate
is r* = 2.75%, the inflation premium for 5-year bonds is IP = 1.65%, the default risk premium for
Niendorf's bonds is DRP = 1.20% versus zero for T-bonds, and the maturity risk premium for all bonds
is found with the formula MRP = (t − 1) × 0.1%, where t = number of years to maturity. What is the
liquidity premium (LP) on Niendorf's bonds?
15 Kop Corporation's 5-year bonds yield 6.50%, and T-bonds with the same maturity yield 4.40%. The
default risk premium for Kop's bonds is DRP = 0.40%, the liquidity premium on Kop's bonds is LP =
1.70% versus zero on T-bonds, the inflation premium (IP) is 1.50%, and the maturity risk premium (MRP)
on 5-year bonds is 0.40%. What is the real risk-free rate, r*?

C. LESSON WRAP-UP
1) Activity 6: Thinking about Learning (5 mins)
Work tracker. Congratulations! You have finished the module for today! Shade the number of the module that
you finished.
First Period Second Period Third Period
1 2 3 4 5 6 7 8 9 10 11 12 13 14 15 16 17 18 19 20 21 22 23 24 25 26

How do you feel today?

I feel (unsatisfactory/satisfactory/excellent) because _______________________________________________________________.

What are your challenges in learning the concepts in this module? If you do not have challenges, what is your
best learning for today?
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________

What are the questions/thoughts you want to share to your teacher today?
______________________________________________________________________________________________________________________
______________________________________________________________________________________________________________________

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

FAQs
1. What is Pure Expectations Theory?
• The pure expectations theory contends that the shape of the yield curve depends on investors’
expectations about future interest rates.
• If interest rates are expected to increase, L-T rates will be higher than S-T rates, and vice-versa. Thus, the
yield curve can slope up, down, or even bow.
2. What are the Assumptions of Pure Expectations?
• Assumes that the maturity risk premium for Treasury securities is zero.
• Long-term rates are an average of current and future short-term rates.
• If the pure expectations theory is correct, you can use the yield curve to “back out” expected future
interest rates.
An Example: Observed Treasury Rates and Pure Expectations

If the pure expectations theory holds, what does the market expect will be the interest rate on one-year securities,
one year from now? Three-year securities, two years from now?

One-Year Forward Rate

(1.062)2 = (1.060) (1 + X)
1.12784/1.060 = (1 + X)
6.4004% =X
• The pure expectations theory says that one-year securities will yield 6.4004%, one year from now.
• Notice, if an arithmetic average is used, the answer is still very close. Solve: 6.2% = (6.0% + X)/2, and the
result will be 6.4%.

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

Three-Year Security, Two Years from Now

(1.065)5 = (1.062)2 (1 + X)3

1.37009/1.12784 = (1 + X)3
6.7005% =X
• The pure expectations theory says that three-year securities will yield 6.7005%, two years from now.

Conclusions About Pure Expectations

• Some would argue that the MRP ≠ 0, and hence the pure expectations theory is incorrect.
• Most evidence supports the general view that lenders prefer S-T securities, and view L-T securities as
riskier.
– Thus, investors demand a premium to persuade them to hold L-T securities (i.e., MRP > 0).

KEY TO CORRECTIONS
Review
P27,408.71

Activity 1 and 4.
What I Know Questions: What I Learned (Activity 4)
What are the determinants r= r* + IP + DRP + LP + MRP
of interest rates? r= required return on a debt security
r*= real risk-free rate of interest
IP= inflation premium
DRP= default risk premium
LP= liquidity premium
MRP= maturity risk premium
What is Pure Expectation The pure expectations theory contends that
Theory? the shape of the yield curve depends on
investors’ expectations about future interest
rates.

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 FIN 072 | Financial Markets
Student Activity Sheet Module #5

Name: _________________________________________________________________ Class number: _______

Section: ____________ Schedule: ________________________________________ Date: ________________

Activity 3.
Activity 3.1. Compare expected return with required and realized return
Risk - The probability that an actual return on an investment will be lower than the expected return Read more:
http://www.businessdictionary.com/definition/risk.html
Expected Return - The process of determining the average expected probability of various different rates of
return that are possible on a given asset. Factors in this determination include different market conditions as well
as an asset's beta. Read more: http://www.businessdictionary.com/definition/expected-return.html
Required Return - Minimum acceptable rate of return on an investment proposal that is comparable with the
rate of return obtainable effortlessly and at a low level of risk in the financial markets (such as on a time deposit
in a bank). Read more: http://www.businessdictionary.com/definition/required-rate-of-return.html
Realized Return - This simple rate of return is sometimes called the basic growth rate, or alternatively, return on
investment, or ROI. If you also consider the effect of the time value of money and inflation, the real rate of return
can also be defined as the net amount of discounted cash flows received on an investment after adjusting for
inflation. https://www.investopedia.com/terms/r/rateofreturn.asp
Activity 3.2. Identify the types of risks
Answer: SR; SR; SR; UR; SR; UR; SR; UR; SR; UR; SR; UR
Activity 3.3. Discuss the concept of standard deviation
Activity 3.3.a. 35.60%; 5.97%; 44.5%; 6.67%
Activity 3.3.b. 14.55%; 22%; 139.16%; 272.80%; 11.80%; 16.52%; 81.10%; 75.10%

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