威廉夏普_投资学课后习题答案解析第五章
合集下载
相关主题
- 1、下载文档前请自行甄别文档内容的完整性，平台不提供额外的编辑、内容补充、找答案等附加服务。
- 2、"仅部分预览"的文档,不可在线预览部分如存在完整性等问题,可反馈申请退款(可完整预览的文档不适用该条件!)。
- 3、如文档侵犯您的权益，请联系客服反馈,我们会尽快为您处理(人工客服工作时间：9:00-18:30)。
Chapter 5 the valuation of riskless securities
Questions and problems
group four -------彭利、蒋英、陈艳 陈红霖、吴晓琴、邹雨薇、陈园华
4、Face value = $1000
n=3
a:① PV = $816.30
V0=$1030 0 INT=$700 P1=$10100 $700 P2=$9900 $700 P3=$9500
rhp
Value at the end of the holding period Value at the beginning of the holding period
-1
方法一：
a. Semianually: Effective interest rate=
r m (1 ) 1 m
6% 2 (1 ) 1 6.09% 2
b. Daily : Effective interest rate=
6% 365 (1 ) 1 6.18% 365
16.a:
24.
s1 9%, s2 7%, es1, 2 4.5%
f1, 2 es1, 2 L1, 2 L1, 2 f1, 2 es1, 2
(1 s2 ) f1, 2 1 1 s1
2
= 5.04%
பைடு நூலகம்
L1, 2 5.04% 4.5% 0.54%
27. Assume that you own a bond that you purchased
-1
=1.1337-1=13.37%
方法二：直接计算出债券在持有期期末的价值。
Step1: how many bonds you can buy at the end of the first year ? You can use the $700 to buy : $700/$10100= 0.0693
1 1 2 d2 (1 s 2 ) 2 d2 (1 s 2 ) 1 (1 s 2 ) 2 d2 1 1 11% 1 s1 1 10%
f 1, 2
1 1 3 d3 (1 s 3 ) 3 d3 (1 s 3 ) f 2,3 (1 s 3 ) 3 1 1 2 d3 (1 s 2 ) 1 1 9.35% d2
3 (1 6.5%)
12. f0,1=S1=10.0%,
f2,3=9.0%,
f1,2=9.5%,
f3,4=8.5%
(1+S2)2=(1+S1)*（1+f1,2） S2=9.75% (1+S3)3=(1+S2)2*(1+f2,3) S3=9.5% (1+S4)4=(1+S3)3*(1+f3,4) S4=9.25%
100 100 1100 997.18 2 1 s1 (1 s 2 ) (1 s3 ) 3 997.18 100d1 100d 2 1100 3 d d 3 0.749
b:
1 d1 0.90909 s1 10% 1 s1 f 0,1 s1 10%
17. 第一问求：bank discount rate (BDR)
∵ PV=FV/(1+i)n
,
n=2 years
∴ $9500/（1+i)2 = $8000 得出i=9% 第二问求:the true interest rate ∵ the true interest rate =BDR/(1-BDR) ∴ the true interest rate =9%/(1-9%)=9.9%
three years ago for $10300. The bond has made three annual interest payments of $700 to you, the last of
which was just paid. At the end of year 1 the bond
13. S1=f0,1=6.0%,f1,2=9.0%,f2,3=10%,
Face value=$1000,i=8%,n=3
$1000* 8% $1000* 8% $1000* 8% $1000 pv (1 6%) (1 6%)(1 9%) (1 6%)(1 9%)(1 10%)
=$801.43+$10876.55=$11677.98
PV=80*0.9434+80*0.8655+1080*0.7868 =$994.46
14.a.
1 dt t (1 st )
1000 909.09 1000d1 1 s1 d1 0.90909
100 1100 991.81 100d1 1100 2 d 2 1 s1 (1 s 2 ) d 2 0.819
持有期期末价值与期初价值之比：
V3 V1 V2 V3 V0 V0 V1 V2 10800 10600 10200 10300 10100 9900 1.1337
rhp
Value at the end of the holding period Value at the beginning of the holding period
So you can obtained $801.43 in interest in the second year and would have had bonds with a Value of $10876.55 at the end of the third year.
Step3: 计算持有期期末价值 value at the end of the holding period
持有期期末价值与期初价值之比：
各时段期末与期初价值之比的积：
V3 V3 V2 V1 V0 V2 V1 V0
V0=$1030 0
INT=$700 P1=$10100
$700 P2=$9900
$700 P3=$9500
During the first year: initial value of bond: V0=$10300 Value of bond at the end of the year:V1=$700+$10100=$10800 During the second year: initial value of bond: V1=$10100 Value of bond at the end of the year:V2=$700+$9900=$10600 During the third year: initial value of bond: V2=$9900 Value of bond at the end of the year:V3=$700+$9500=$10200
9.
pt
mt (1 st )
t
t mt (1 st ) pt
t mt (1 st ) pt
dt 1
t (1 st )
pt dt mt
pt dt mt
M t $1000
(1).Three year bonds:
P3 $810.60
$810.60 d3 0.8160 $1000
t (1 st ) f t 1,t 1 t 1 (1 st 1 )
(1 5.5%) f1.2 1 6% (1 5%) f 2,3 f 3,4
3 (1 6.5%) 2 (1 5.5%) 4
2
1 8.53% 1 8.51%
(1 7%)
第二年末收到的利息=1.0693*700= $748.51
第二年末持有的债券的价值=1.0693*9900= $10532.61
So you can obtained $748.51 in interest in the second year and would have had bonds with a Value of $10532.61 at the end of the second year.
n=4
b:①
r1 12% 100 100 100 100 PV1 2 3 (1 12%) (1 12%) (1 12%) (1 12%)4 89.29 79.72 71.18 699.07 939.26
②
r2 8% 100 100 100 100 PV2 2 3 (1 8%) (1 8%) (1 8%) (1 8%)4 92.59 85.73 79.38 808.53 1066 23 .
PV=$30000
0
1
2
3
8%
10%
12%
FV=30000 (1+8%)（1+10%）(1+12%)= $ 39916.8
b:
PV=$30000 4% 4%
1 5% 5%
2 6% 6%
3
FV PV (1 i ) n 8% 2 10% 2 12% 2 FV $30000 (1 ) (1 ) (1 ) $4019558 . 2 2 2
sold for $10100. At the end of year 2, it sold for $9900. The bond now sells for $9500. what was your holding-period return over the three-year period?
7. face value=$1000, i=9%, n=3,
PV=$975.13, PMT=1000×9%=90
90 90 1090 975.13 2 3 1 r (1 r ) (1 r ) r 10%
8. face value=$1000, n=3,
PV1=$930.23, PV2=$923.79, PV3=$919.54
c:
500 600 700 P 2 3 1 s1 (1 s 2 ) (1 s3 ) 500 d1 600 d 2 700 d 3 500 0.909 600 0.819 700 0.749 1470.2
15.
Effective interest rate=
FV PV (1 S t ) t $1000 PV1 $930.23 S1 7.5% 1 (1 S1 ) $1000 PV2 $923.79 S 2 4 .0 % 2 2 (1 S ) $1000 PV3 $919.54 S 3 2.84% 3 (1 S 3 )
816.30 1000 3 (1 ra ) ra 7%
② PV = $949.37 PMT = 70
70 70 1070 949.37 2 (1 rb ) (1 rb ) (1 rb )3 rb 9%
插补法
Face value = $1000
PMT = 100
Step2: how many bonds you can buy at the end of the second year ?
You can use the $748.51 to buy: $748.51/$9900 =0.0756
第三年末收到的利息= (1.0693+0.0756)*700=$801.43 第三年末持有的债券的价值：= (1.0693+0.0756)*9500 = $10876.55
The four-year bonds:
p 4 $730.96 $730.96 d4 0.73096 $1000
The five-year bonds
p 5 $649.93 $649.93 d5 0.64993 $1000
11.
t (1 st ) (1 f (t 1,t ) ) t 1 (1 st 1 )
Questions and problems
group four -------彭利、蒋英、陈艳 陈红霖、吴晓琴、邹雨薇、陈园华
4、Face value = $1000
n=3
a:① PV = $816.30
V0=$1030 0 INT=$700 P1=$10100 $700 P2=$9900 $700 P3=$9500
rhp
Value at the end of the holding period Value at the beginning of the holding period
-1
方法一：
a. Semianually: Effective interest rate=
r m (1 ) 1 m
6% 2 (1 ) 1 6.09% 2
b. Daily : Effective interest rate=
6% 365 (1 ) 1 6.18% 365
16.a:
24.
s1 9%, s2 7%, es1, 2 4.5%
f1, 2 es1, 2 L1, 2 L1, 2 f1, 2 es1, 2
(1 s2 ) f1, 2 1 1 s1
2
= 5.04%
பைடு நூலகம்
L1, 2 5.04% 4.5% 0.54%
27. Assume that you own a bond that you purchased
-1
=1.1337-1=13.37%
方法二：直接计算出债券在持有期期末的价值。
Step1: how many bonds you can buy at the end of the first year ? You can use the $700 to buy : $700/$10100= 0.0693
1 1 2 d2 (1 s 2 ) 2 d2 (1 s 2 ) 1 (1 s 2 ) 2 d2 1 1 11% 1 s1 1 10%
f 1, 2
1 1 3 d3 (1 s 3 ) 3 d3 (1 s 3 ) f 2,3 (1 s 3 ) 3 1 1 2 d3 (1 s 2 ) 1 1 9.35% d2
3 (1 6.5%)
12. f0,1=S1=10.0%,
f2,3=9.0%,
f1,2=9.5%,
f3,4=8.5%
(1+S2)2=(1+S1)*（1+f1,2） S2=9.75% (1+S3)3=(1+S2)2*(1+f2,3) S3=9.5% (1+S4)4=(1+S3)3*(1+f3,4) S4=9.25%
100 100 1100 997.18 2 1 s1 (1 s 2 ) (1 s3 ) 3 997.18 100d1 100d 2 1100 3 d d 3 0.749
b:
1 d1 0.90909 s1 10% 1 s1 f 0,1 s1 10%
17. 第一问求：bank discount rate (BDR)
∵ PV=FV/(1+i)n
,
n=2 years
∴ $9500/（1+i)2 = $8000 得出i=9% 第二问求:the true interest rate ∵ the true interest rate =BDR/(1-BDR) ∴ the true interest rate =9%/(1-9%)=9.9%
three years ago for $10300. The bond has made three annual interest payments of $700 to you, the last of
which was just paid. At the end of year 1 the bond
13. S1=f0,1=6.0%,f1,2=9.0%,f2,3=10%,
Face value=$1000,i=8%,n=3
$1000* 8% $1000* 8% $1000* 8% $1000 pv (1 6%) (1 6%)(1 9%) (1 6%)(1 9%)(1 10%)
=$801.43+$10876.55=$11677.98
PV=80*0.9434+80*0.8655+1080*0.7868 =$994.46
14.a.
1 dt t (1 st )
1000 909.09 1000d1 1 s1 d1 0.90909
100 1100 991.81 100d1 1100 2 d 2 1 s1 (1 s 2 ) d 2 0.819
持有期期末价值与期初价值之比：
V3 V1 V2 V3 V0 V0 V1 V2 10800 10600 10200 10300 10100 9900 1.1337
rhp
Value at the end of the holding period Value at the beginning of the holding period
So you can obtained $801.43 in interest in the second year and would have had bonds with a Value of $10876.55 at the end of the third year.
Step3: 计算持有期期末价值 value at the end of the holding period
持有期期末价值与期初价值之比：
各时段期末与期初价值之比的积：
V3 V3 V2 V1 V0 V2 V1 V0
V0=$1030 0
INT=$700 P1=$10100
$700 P2=$9900
$700 P3=$9500
During the first year: initial value of bond: V0=$10300 Value of bond at the end of the year:V1=$700+$10100=$10800 During the second year: initial value of bond: V1=$10100 Value of bond at the end of the year:V2=$700+$9900=$10600 During the third year: initial value of bond: V2=$9900 Value of bond at the end of the year:V3=$700+$9500=$10200
9.
pt
mt (1 st )
t
t mt (1 st ) pt
t mt (1 st ) pt
dt 1
t (1 st )
pt dt mt
pt dt mt
M t $1000
(1).Three year bonds:
P3 $810.60
$810.60 d3 0.8160 $1000
t (1 st ) f t 1,t 1 t 1 (1 st 1 )
(1 5.5%) f1.2 1 6% (1 5%) f 2,3 f 3,4
3 (1 6.5%) 2 (1 5.5%) 4
2
1 8.53% 1 8.51%
(1 7%)
第二年末收到的利息=1.0693*700= $748.51
第二年末持有的债券的价值=1.0693*9900= $10532.61
So you can obtained $748.51 in interest in the second year and would have had bonds with a Value of $10532.61 at the end of the second year.
n=4
b:①
r1 12% 100 100 100 100 PV1 2 3 (1 12%) (1 12%) (1 12%) (1 12%)4 89.29 79.72 71.18 699.07 939.26
②
r2 8% 100 100 100 100 PV2 2 3 (1 8%) (1 8%) (1 8%) (1 8%)4 92.59 85.73 79.38 808.53 1066 23 .
PV=$30000
0
1
2
3
8%
10%
12%
FV=30000 (1+8%)（1+10%）(1+12%)= $ 39916.8
b:
PV=$30000 4% 4%
1 5% 5%
2 6% 6%
3
FV PV (1 i ) n 8% 2 10% 2 12% 2 FV $30000 (1 ) (1 ) (1 ) $4019558 . 2 2 2
sold for $10100. At the end of year 2, it sold for $9900. The bond now sells for $9500. what was your holding-period return over the three-year period?
7. face value=$1000, i=9%, n=3,
PV=$975.13, PMT=1000×9%=90
90 90 1090 975.13 2 3 1 r (1 r ) (1 r ) r 10%
8. face value=$1000, n=3,
PV1=$930.23, PV2=$923.79, PV3=$919.54
c:
500 600 700 P 2 3 1 s1 (1 s 2 ) (1 s3 ) 500 d1 600 d 2 700 d 3 500 0.909 600 0.819 700 0.749 1470.2
15.
Effective interest rate=
FV PV (1 S t ) t $1000 PV1 $930.23 S1 7.5% 1 (1 S1 ) $1000 PV2 $923.79 S 2 4 .0 % 2 2 (1 S ) $1000 PV3 $919.54 S 3 2.84% 3 (1 S 3 )
816.30 1000 3 (1 ra ) ra 7%
② PV = $949.37 PMT = 70
70 70 1070 949.37 2 (1 rb ) (1 rb ) (1 rb )3 rb 9%
插补法
Face value = $1000
PMT = 100
Step2: how many bonds you can buy at the end of the second year ?
You can use the $748.51 to buy: $748.51/$9900 =0.0756
第三年末收到的利息= (1.0693+0.0756)*700=$801.43 第三年末持有的债券的价值：= (1.0693+0.0756)*9500 = $10876.55
The four-year bonds:
p 4 $730.96 $730.96 d4 0.73096 $1000
The five-year bonds
p 5 $649.93 $649.93 d5 0.64993 $1000
11.
t (1 st ) (1 f (t 1,t ) ) t 1 (1 st 1 )