2. This problem demonstrates one approach to show R* +R{Re* = Rƒ. (a) Write any return R as R* + (R-R) and use the fact that 1- Re* is orthogonal to excess returns-recall that Re* represents the expectation operator on the space of excess returns to show that 1 X (1 - R*) E[R*] is an SDF. (b) When there is a risk-free asset, X defined above, being spanned by a constant and an excess return, is in the span of the returns and hence must equal X*. Use this fact to demonstrate R* + R+Re* = Rƒ. (Hint: E [(R¢*)²] = E[Re*] may be useful.)
2. This problem demonstrates one approach to show R* +R{Re* = Rƒ. (a) Write any return R as R* + (R-R) and use the fact that 1- Re* is orthogonal to excess returns-recall that Re* represents the expectation operator on the space of excess returns to show that 1 X (1 - R*) E[R*] is an SDF. (b) When there is a risk-free asset, X defined above, being spanned by a constant and an excess return, is in the span of the returns and hence must equal X*. Use this fact to demonstrate R* + R+Re* = Rƒ. (Hint: E [(R¢*)²] = E[Re*] may be useful.)
Essentials Of Investments
11th Edition
ISBN:9781260013924
Author:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Publisher:Bodie, Zvi, Kane, Alex, MARCUS, Alan J.
Chapter1: Investments: Background And Issues
Section: Chapter Questions
Problem 1PS
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![2. This problem demonstrates one approach to show R* + R;Re* = Rf.
(a) Write any return R as R* + (R – R*) and use the fact that 1 – Re* is orthogonal
to excess returns recall that R°* represents the expectation operator on the space of
excess returns-to show that
1
(1 – Rº*)
E[R*]
X =
is an SDF.
(b) When there is a risk-free asset, X defined above, being spanned by a constant and an
excess return, is in the span of the returns and hence must equal X*. Use this fact to
demonstrate R" + R;Rº* = R;. (Hint: E (R*)° = E[R*] may be useful.)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F0970bad0-04d4-4db5-8ddb-1f9d1ee5455a%2Fc19a88e5-1771-47bc-b179-10a0dffd2e00%2Fojzfr1l_processed.png&w=3840&q=75)
Transcribed Image Text:2. This problem demonstrates one approach to show R* + R;Re* = Rf.
(a) Write any return R as R* + (R – R*) and use the fact that 1 – Re* is orthogonal
to excess returns recall that R°* represents the expectation operator on the space of
excess returns-to show that
1
(1 – Rº*)
E[R*]
X =
is an SDF.
(b) When there is a risk-free asset, X defined above, being spanned by a constant and an
excess return, is in the span of the returns and hence must equal X*. Use this fact to
demonstrate R" + R;Rº* = R;. (Hint: E (R*)° = E[R*] may be useful.)
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