ְм

¡Ͷʸ

¿
ΪͶʹĻ½ڣǺµĻҪǿ͹ͼ⣬ĿҪʱʲģͺͶʺͶϱ׼ļ㡣

һͶʵĺ

ڵҪݣ
һͶʵĺص㣨˽⣩
ͶʵĶգ
ͶͶʵĹϵ˽⣩
ġͶʵķࣨգ

һͶʵĺص
1壺ͶʾҵΪȡһͶʽľΪ
2ص㣺Ŀԡʱԡԡ

Ͷʶķ

׼
ͶʵIJ	ΪöսԶ
ͶʵĹ	ŶɢնͿƶ

ͶͶʵĹϵ
ͶһֳеջȡΪ

ͶͶʵĹϵ		Ͷ
ͬ
ͶͶʵһʽߵĿĻһ£ߵδ涼вȷԣзأҪеʧΣա	ͶͶΪ޵ij̡۵㡢еյĴСͽ׵ķʽȷ	ھУͶ𵽵ƽ⡢á	ͶΥͶڲᰲгҺγĭõá

ġͶʵķࣨעͶʵص㣩

׼
ͶΪĽ̶Ȳͬ	ֱͶ	ʽߺʽʹͳһ
	Ͷ	ʽߺʽʹǷ
ͶʶIJͬ	ʵͶ	ͶʶΪʵ̬ʲڽͶʵķСԵ͡׳ɱ
	Ͷ	ͶʶΪʲʵͶʵķմԸߡ׳ɱ
Ͷͬ	Ͷ	ճɹΪʲ
	Ͷ	ճɹΪʲγγѻ
ӪĿIJͬ	ӯͶ	ŴٽչҪְ
	Ͷ	ܴЧ棬ȴܴЧ
Ͷʵķͬ	Ͷ	ҵͨͶʿʹҵȡÿɹҵʹõʵʲ
	Ͷ	ҵͶʲʹҵȡÿɹҵʹõʵʲ
Ͷʵݲͬ	̶ʲͶʡʲͶʡͶʡʽͶʡزͶʡм֤ȯͶʡڻȨͶʡͶʡͶʵȶʽ

ڶͶʷͶ

һͶʷյĺ
Ͷĺ
ͶϷʵļ

һͶʷյĺ
1壺ͶʷָͶʻֲܵȷصĹͬӰ죬ʹʵͶʳֲĿԡ
2ͶʷղԭͶʳɱIJȷԡͶIJȷԡг仯µĹպʷաηպȻֺԼͶʾʧȶ档

Ͷĺ
ͶֳͶʱָ꣬ͶߴͶлȡIJͶ桢ʵͶ桢޷ͱҪͶ͡
ͶָͶ治ȷ£Ƶĸֿˮƽ䷢ĸʼļȨƽ
ʵͶָضͶĿʵʩ֮һʱڵõʵ棬ֳʵͶ棻
޷=ʽʱֵ+ͨͲ

ͶϷʵļ
ͶͬʱʲΪͶʶͶʣͶϡͬʱֻϵм֤ȯΪͶʶ󣬳Ϊ֤ȯϡ
1Ͷϵ
ͶϵʾͶϵĸͶĿʵļȨƽȨڸͶĿͶܶռı乫ʽ

[5-1]Ͷϵʵļ
ijҵֱͶAʲBʲУͶAʲΪ8%ƻͶʶΪ500ԪͶBʲΪ12%ƻͶʶΪ500Ԫ
Ҫ󣺼Ͷϵʡ

2ʲɵͶϵķ
1Э
ЭһڲͶijһͶĿһͶĿյͳָꡣ㹫ʽΪ

ۣЭļΪֵҲΪֵǷֱʾͶĿ֮ʱ䶯ķ򡣵ЭΪֵʱʾʲʳͬ䶯ЭΪֵʱʾʲʳ෴仯ЭľֵԽ󣬱ʾʲʵĹϵԽУЭľֵԽСʲʾԽԶ
2ϵ
ϵЭͶʷͶ׼֮ıֵ㹫ʽΪ

ϵ-1+1֮ķΧڱ䶯1ȫأ+1ȫأ0ʾء
ϵЭĹϵ

3ʲɵͶϵܷ
ͶϵܷͶʵķͱ׼ʲ϶ɵͶʷļ㹫ʽΪ

ʲ϶ɵͶʵı׼ļ㹫ʽΪ

5-2ʲĹɵͶϵķۡ
԰5-1ϡٶͶABʲʵı׼Ϊ9%
Ҫ󣺷ֱ㵱ABʲϵֱΪ+1+0.4+0.10-0.1-0.4-1ʱͶʵЭͱ׼
⣺⣬W1=50%,W2=50%1929
Cov(R1R2)0.09×0.09×12=0.008112
0.52×0.0920.52×0.0922×0.5×0.5×Cov(R1R2)
0.004050.5Cov(R1R2)
׼0.004050.5Cov(R1R2)1/2
121ʱ
Cov(R1R2)0.0081×10.0081
Vp0.004050.5×0.00810.0081
p=0.00811/2=0.09
ͬɼϵֱΪ+0.4+0.10-0.1-0.4-1ʱЭͱ׼ֵ5-1ʾ

ϵ	1	0.4	0.1	0	-0.1	-0.4	-1
Э	0.0081	0.00324	0.00081		-0.00081	-0.00324	-0.0081
	0.0081	0.00567	0.004455	0.00405	0.003645	0.00243
׼	0.09	0.075299	0.066746	0.06364	0.060374	0.49295

ۣϵӰͶϵʣӰϷաͶʲ֮ϵΣֻҪͶʱ䣬ʲʲ䣬ͶϵʾͲ䣬10%ڲͬϵͶʵı׼ȴ֮仯
ϵΪ+1ʱʲʵı仯䶯ȫͬһͬ½ܵκͶʷա
ϵΪ-1ʱպ෴ʲʵı仯䶯ȫ෴Ϊ˼ȫȫͶʷա
ϵ0+1Χڱ䶯ʱʲ֮عϵ֮س̶ԽͣͶϿɷɢͶʷյЧԽ
ϵ0-1Χڱ䶯ʱʲ֮Ǹعϵ֮ĸس̶ԽֵͣԽСͶϿɷɢͶʷյЧԽС
ϵΪʱʲ֮޹ء
1ijҵͶABͶĿй£

Ŀ	A	B
	10%	18%
׼	12%	20%
Ͷʱ	0.8	0.2
ABϵ	0.2

Ҫ
1ͶAB
2ABЭ
3ABϷ(ٷλλС)
4ABϱ׼(ٷλλС)
1=Ȩƽ=10%×0.8+18%×0.2=11.6%
2Э=12%×20%×0.2=0.48%
3Ϸ=
=1.2352%
4ϱ׼==11.11%
3ʲɵͶϵķռɢ
Ͷϵܷɷϵͳպϵͳɡ
ϵͳ(ɷɢ)ָijһضԭijһضʲӰĿԡͨɢͶʣϵͳԷܹͣɢЧĻַվܱȫϵͳյľ幹ݰӪպͲ֡
ϵͳ(ɷɢ)ָг仯гʲʵı䶯ԣЩӰгķģֳΪгաϵͳӰʲķգܱɢ

ʱʲģ

Ҫ
һϵ
ʱʲģ
һϵ
һʲĦϵ˽⣩
1
ʲĦϵָԷӳʲгȫʲƽ֮䶯ϵһָ꣬ʲϵͳնгƽյӰ̶ȣҲΪϵͳָ
2
ʽ1

ʽ2

3
£1ʱʾõʲгƽʳͬı仯гͶϵķһ££1˵õʲķմгͶϵķգ£1˵õʲķճ̶СгͶϵķա
ͶϵĦϵգ
1.
ͶϵĦϵеʲϵļȨƽȨΪʲͶռıء
2.㣺
5-3Ͷϵļ--һ
ijͶABCʲɣйػĸʲĦϵֱΪ0.51.01.2ʲͶеıطֱΪ10%30%60%
Ҫ󣺼ͶϵĦϵ
⣺ͶϵĦϵ0.5×101.0×301.2×601.07
3.ӰأͶϵĦϵܵʲĦϵ͸ʲͶռصӰ졣

ʱʲģ
1.ʱʲģ͵Ļʽ

ʲضͶϵıҪܵ޷ʡгϵƽʺͦϵصӰ졣
5-4AƱĦϵΪ0.5BƱĦϵΪ1.0CƱĦϵΪ2޷Ϊ6%ٶͬгйƱƽΪ10%
Ҫ󣺼ֹƱıҪʣжϵЩƱʷֱﵽʱͶ߲ԸͶʹ
⣺AƱıҪʣ60.5×1068
BƱıҪʣ61.0×10610
CƱıҪʣ62×10614
ֻеAƱʴﵽ򳬹8%BƱʴﵽ򳬹10%CƱʴﵽ򳬹14%ʱͶ߲ԸͶʹ򡣷Ͷ߾ͲͶʡ
2.ͶϷʵļ
ͶϷʵļ㹫ʽΪ

ͶϷҲܵгϵƽʡ޷ʺͶϵĦϵصӰ졣ز£ͶϵĦϵȡϵԽ󣬷ʾԽ󣻷֮ԽС
5-5ijҵĿǰABCֹƱɵ֤ȯϣÿֻƱĦϵֱ0.51.01.2֤ȯռıطֱΪ10%30%60%ݴ˼֤ȯϵĦϵΪ1.07ǰƱгΪ10%޷Ϊ6%
Ҫ󣺼ù˾֤ȯϵķ
⣺⣬,
֤ȯϵķ

5-6԰5-5ϣù˾Ϊͷգ۳CƱAƱʹABCֹƱ֤ȯռıرΪ60%30%10%䡣
Ҫ
1֤ȯϵĦϵ
2֤ȯϵķʣԭϽбȽϡ
⣺1֤ȯϵĦϵ0.5×601.0×301.2×100.72
2֤ȯϵķʣ0.72×1062.88
Ϊ֤ȯϵķΪ2.88Сԭϵ4.28˵ϵͳձˡ
ӱпԿıͶʱأӰͶϵĦϵıʡ
3.ͶϦϵ㣺

ʱʲģݵļ˽⣩
1гдͶߣ
2Ͷ߶ƻֻһڳʲ
3Ͷֻܽ׹׵ĽڹߣƱծȯȣٶͶ߿ԲƵԹ̶޷ʽ
4гĦ
5еͶ߶ԵģҶܻϢ
6еͶ߶ͬĹ۵ͷԴͶʹߣǶ׵ĽڹδֽĸʷֲԤֵͷȶͬĹơ
ܵ˵ʱʲģǽгԺͻûĦĻ֮ϵġ
⡳ij˾ͶABCDEֹƱռıֱ10%20%20%30%20%ЦϵֱΪ0.811.41.51.7ƱƽյıҪΪ16%޷Ϊ10%
Ҫ
1ֹƱԵıҪʣ
2ͶϵۺϦϵ
3Ͷϵķʣ
4ͶϵıҪʡ
𰸣1
RA=10%+0.8×16%-10%=14.8%
RB=10%+1×16%-10%=16%
RC=10%+1.4×16%-10%=18.4%
RD=10%+1.5×16%-10%=19%
RE=10%+1.7×16%-10%=20.2%
2ۺϦϵ
=10%×0.8+20%×1+20%×1.4+30%×1.5+20%×1.7=1.35
3Ͷϵķ=1.35×16%-10%=8.1%
4ͶϵıҪ=10%+8.1%18.1%