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Bodie_Essentials_of_Investments_11e_Ch05_SM.docx-Chapter 05 - Risk and Return:
Page 1
Chapter 05 - Risk and Return: Past and Prologue
CHAPTER 05
RISK AND RETURN: PAST AND PROLOGUE
1.
The 1% VaR will be less than –30%. As percentile or probability of a return declines so
does the magnitude of that return. Thus, a 1 percentile probability will produce a
smaller VaR than a 5 percentile probability.
2.
If inflation increases from 3% to 5%, according to the Fisher equation there will be a
concurrent increase in the nominal rate to offsets the increase in expected inflation.
This gives investors an unchanged growth of purchasing power.
3.
The excess return on the portfolio will be the same as long as you are consistent: you
can use either real rates for the returns on both the portfolio and the risk-free asset, or
nominal rate for each. Just don’t mix and match!
So the average excess return, the
numerator of the Sharpe ratio, will be unaffected.
Similarly, the standard deviation of
the excess return also will be unaffected, again as long as you are consistent.
4.
Decrease. Typically, standard deviation exceeds return. Thus, an underestimation of 4%
in each will artificially decrease the return per unit of risk. To return to the proper risk
return relationship the portfolio will need to decrease the amount of risk free
investments.
5.
Using Equation 5.10, we can calculate the mean of the HPR as:
E(r) =
s
=
1
S
p(s) r(s)
= (0.3
0.44) + (0.4
0.14) + [0.3
(–0.16)] = 0.14 or 14%
Using Equation 5.11, we can calculate the variance as:
Var(r) =
2
=
s
=
1
S
p(s) [ r(s)
– E(r)]
2
= [0.3
(0.44 – 0.14)
2
] + [0.4
(0.14 – 0.14)
2
] + [0.3
(–0.16 – 0.14)
2
]
= 0.054
SD(r) =
=
Var ( r)
=
0.054
= 0.2324 or 23.24% [Standard Deviation]
6.
We use the below equation to calculate the holding period return of each scenario:
HPR =
Ending Price
Beginning Price + Cash Dividend
Be ginning Price
a.
The holding period returns for the three scenarios are:
Boom:
(50 – 40 + 2)/40 = 0.30 = 30%
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consent of McGraw-Hill Education.


Page 2
Chapter 05 - Risk and Return: Past and Prologue
Normal:
(43 – 40 + 1)/40 = 0.10 = 10%
Recession: (34 – 40 + 0.50)/40 = –0.1375 = –13.75%
E(HPR) =
s
=
1
S
p(s) r(s)
= [(1/3)
0.30] + [(1/3)
0.10] + [(1/3)
(–0.1375)]
= 0.0875 or 8.75%
Var(HPR)
=
s
=
1
S
p(s) [ r(s)
– E(r)]
2
= [(1/3)
(0.30 – 0.0875)
2
] + [(1/3)
(0.10 – 0.0875)
2
]
+ [(1/3) (–0.1375 – 0.0875)
2
]
= 0.031979
SD(r) =
=
Var ( r)
=
¿
= 0.1788 or 17.88%
b.
E(r) = (0.5
8.75%) + (0.5
4%) = 6.375%
= 0.5
17.88% = 8.94%
7.
a.
Time-weighted average returns are based on year-by-year rates of return.
Year
Return = [(Capital gains + Dividend)/Price]
2010-2011
(110 – 100 + 4)/100 = 0.14 or 14.00%
2011-2012
(90 – 110 + 4)/110 = –0.1455 or –14.55%
2012-2013
(95 – 90 + 4)/90 = 0.10 or 10.00%
Arithmetic mean: [0.14 + (–0.1455) + 0.10]/3 = 0.0315 or 3.15%
Geometric mean:
3
(1 + 0.14)
[1 + ( –0.1455)]
(1 + 0.10)
– 1
= 0.0233 or 2.33%
b.
Date
1/1/2010
1/1/2011
1/1/2012
1/1/2013
Net Cash Flow
–300
–208
110
396
Time
Net Cash flow
Explanation
0
–300
Purchase of three shares at $100 per share
1
–208
Purchase of two shares at $110,
plus dividend income on three shares held
2
110
Dividends on five shares,
Copyright © 2019 McGraw-Hill Education. All rights reserved. No reproduction or distribution without the prior written
consent of McGraw-Hill Education.


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