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Assignment 08 – Risk and Return
BU340 – Managerial Finance
Directions: Unless otherwise stated, answer in complete
sentences, and be sure to use co
ect English spelling and
grammar. Sources must be cited in APA format. Your response
should be four (4) pages in length.
Respond to the items below.
Part A: Moore Company is about to issue a bond with
semiannual coupon payments, a coupon rate of 8%, and par
value of $1,000. The yield-to-maturity for this bond is 10%.
a. What is the price of the bond if the bond matures in 5, 10, 15,
or 20 years?
. What do you notice about the price of the bond in relationship
to the maturity of the bond?
Part B: The Crescent Corporation just paid a dividend of $2 per
share and is expected to continue paying the same amount each
year for the next four years. If you have a required rate of return
of 13%, plan to hold the stock for four years, and are confident
that it will sell for $30 at the end of four years, how much
should you offer to buy it at today?
Part C: Use the information in the following table to answer the
questions below:
State of
Economy
Probability
of State
Return
on A in
State
Return
on B in
State
Return
on C in
State
Boom XXXXXXXXXX300
Normal XXXXXXXXXX200
Recession XXXXXXXXXX.260
a. What is the expected return of each asset?
. What is the variance of each asset?
c. What is the standard deviation of each asset?
BU340V Chapter 8.pptx
Financial Management: Core Concepts
Fourth Edition
Chapter 8
Risk and Return
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Learning Objectives (1 of 2)
8.1 Calculate profits and returns on an investment and convert holding period returns to annual returns.
8.2 Define risk and explain how uncertainty relates to risk.
8.3 Appreciate the historical returns of various investment choices.
8.4 Calculate standard deviations and variances with historical data.
8.5 Calculate expected returns and variances with conditional returns and probabilities.
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Learning Objectives (2 of 2)
8.6 Interpret the trade-off between risk and return.
8.7 Understand when and why diversification works at minimizing risk, and understand the difference between systematic and unsystematic risk.
8.8 Explain beta as a measure of risk in a well-diversified portfolio.
8.9 Illustrate how the security market line and the capital asset pricing model represent the two-parameter world of risk and return.
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8.1 Returns
Performance analysis of an investment requires investors to measure returns over time.
Return and risk being intricately related, return measurement helps in the understanding of investment risk.
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8.1 (A) Dollar Profits and Percentage Returns (1 of 4)
Dollar profit or loss = Ending value + Distributions − Original cost
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8.1 (A) Dollar Profits and Percentage Returns (2 of 4)
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8.1 (A) Dollar Profits and Percentage Returns (3 of 4)
Example 1: Calculating Dollar and Percentage Returns
Joe bought some gold coins for $1000 and sold those 4 months later for $1200.
Jane on the other hand bought 100 shares of a stock for $10 and sold those 2 years later for $12 per share after receiving $0.50 per share as dividends for the year.
Calculate the dollar profit and percent return earned by each investor over their respective holding periods.
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8.1 (A) Dollar Profits and Percentage Returns (4 of 4)
Example 1: Answe
Joe’s Dollar profit = Ending value − Original cost
= $1200 − $1000 = $200
Joe’s HPR = Dollar profit ÷ Original cost
= $200 ÷ $1000 = 20%
Jane’s Dollar profit = Ending value + Distributions − Original cost
= $12 × 100 + $0.50 × 100 − $10 × 100
= $1200 + $50 − $1000
= $250
Jane’s HPR = $250 ÷ $1000 = 25%
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8.1 (B) Converting Holding Period Returns to Annual Returns (1 of 3)
With varying holding periods, holding period returns not good for comparison.
Necessary to state an investment’s performance in terms of an annual percentage rate (APR) or an effective annual rate of return (EAR) by using the following conversion formulas:
Simple annual return or APR = HPR ÷ n
EAR = (1 + HPR)1 ÷ n − 1
Where n is the number of years or proportion of a year that the holding period consists of.
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8.1 (B) Converting Holding Period Returns to Annual Returns (2 of 3)
Example 2: Comparing HPRs
Given Joe’s HPR of 20% over 4 months and Jane’s HPR of 25% over 2 years, is it co
ect to conclude that Jane’s investment performance was better than that of Joe?
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8.1 (B) Converting Holding Period Returns to Annual Returns (3 of 3)
Example 2: Answe
Compute each investor’s APR and EAR and then make the comparison.
Joe’s holding period (n) = 4 ÷ 12 = 0.333 years
Joe’s APR = HPR ÷ n = 20% ÷ 0.333 = 60%
Joe’s EAR = (1 + HPR)1 ÷ n − 1 = XXXXXXXXXX ÷ .33 − 1 = 72.89%
Jane’s holding period = 2 years
Jane’s APR = HPR ÷ n = 25% ÷ 2 = 12.5%
Jane’s EAR = (1 + HPR)1 ÷ n − 1 = XXXXXXXXXX ÷ 2 − 1 = 11.8%
Clearly, on an annual basis, Joe’s investment far outperformed Jane’s investment.
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8.1 (C) Extrapolating Holding Period Returns (1 of 2)
Extrapolating short-term HPRs into APRs and EARs is mathematically co
ect, but often unrealistic and infeasible.
Implies earning the same periodic rate over and over again in 1 year.
A short holding period with fairly high HPR would lead to huge numbers if return is extrapolated.
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8.1 (C) Extrapolating Holding Period Returns (2 of 2)
Example 3: Unrealistic Nature of APR and EAR.
Let’s say you buy a share of stock for $2 and sell it a week later for $2.50. Calculate your HPR, APR, and EAR. How realistic are the numbers?
N = 1 ÷ 52 or XXXXXXXXXXof 1 year.
Profit = $2.50 − $2.00 = $0.50
HPR = $0.5 ÷ $2.00 × 100 = 25%
APR = 25% ÷ XXXXXXXXXX = 1300% or
= 25% × 52 weeks = 1300%
EAR = (1 + HPR)52 − 1
= XXXXXXXXXX − 1 × 100 = 10,947,544.25%
Answer: Highly Improbable!
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8.2 Risk (Certainty and Uncertainty)
Future performance of most investments is uncertain.
Risky → Potential for loss exists
Risk can be defined as a measure of the uncertainty in a set of potential outcomes for an event in which there is a chance of some loss.
It is important to measure and analyze the risk potential of an investment, so as to make an informed decision.
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8.3 Historical Returns (1 of 2)
Figure 8.1 Histograms of (A) U.S. Treasury bills from 1950 to 1999, (B) long-term government bonds from 1950 to 1999, (C) large company stocks from 1950 to 1999, and (D) small company stocks from 1950 to 1999.
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8.3 Historical Returns (2 of 2)
Small company stocks earned the highest average return (17.10%) over the 5 decades, but also had the greatest variability 29.04%, and widest range.
(103.39% − (−40.54%)) = 143.93%), and were most spread out.
Three-month treasury bills earned the lowest average return, 5.23%, but their returns had very low variability (2.98%), a very small range (14.95%−0.86% = 15.91%) and were much closely clustered around the mean.
Returns and risk are positively related.
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8.4 Standard Deviation as a Measure of Risk (1 of 4)
Variance and standard deviation are measures of dispersion.
Helps researchers determine how spread out or clustered together a set of numbers or outcomes is around their mean or average value.
The larger the variance, the greater is the variability and hence the riskiness of a set of values.
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8.4 Standard Deviation as a Measure of Risk (2 of 4)
Example 4: Calculating the Variance of Returns for Large-Company Stocks
Listed below are the annual returns associated with the large-company stock portfolio from 1990 to 1999. Calculate the variance and standard deviation of the returns.
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8.4 Standard Deviation as a Measure of Risk (3 of 4)
Year Return (R-Mean) (R-Mean)2
1990 −3.20% −22.19% XXXXXXXXXX
1991 30.66% 11.67% XXXXXXXXXX
1992 7.71% −11.28% XXXXXXXXXX
1993 9.87% −9.12% XXXXXXXXXX
1994 1.29% −17.70% XXXXXXXXXX
1995 37.71% 18.72% XXXXXXXXXX
1996 23.07% 4.08% XXXXXXXXXX
1997 33.17% 14.18% XXXXXXXXXX
1998 28.58% 9.59% XXXXXXXXXX
1999 21.04% 2.05% XXXXXXXXXX
Total 189.90% Blank XXXXXXXXXX
Average 18.99% Blank Blank
Variance XXXXXXXXXX Blank Blank
Std. Dev 14.207% Blank Blank
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8.4 Standard Deviation as a Measure of Risk (4 of 4)
Example 4: Answe
Variance = ∑(R-Mean)2 ÷ N − 1
= XXXXXXXXXX ÷ 10 − 1
= XXXXXXXXXX
Std. Dev. = √Variance
= √ XXXXXXXXXX = 14.207%
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