• (1+11/2)2-0.5 (1+12/2)2-2 P CF₁ CF₂ - + + + CFT CF1 CF2 = (1+ytm/2)1-2 (1+ytm/2)2-2 + + (1+r7/2)1-2 CFT (1+ytm/2)1-2 + P= (w1, 1,, Wn) ⇒ Duration: = w₁ D₁+w2 ⋅ D₂+ ... + Wn · Dn AP/P-Durp Ay . •AP/P-Durp Ay + ½ Convexity (Ay)² wo . • ΨΑ = where w = 1+wo(1-BA) αA/02(EA) E(rm-rƒ)/0²(rm)* WM = 1 - WA. • t-statistic = estimate-null value standard error • If t>2, then p-value < 0.05 • P = D₁ = E₁x (1- b) Formulas and facts: ⚫ Accrued interest = (#days since last coupon/number of days per coupon period)*coupon • CAPM: E(ra) = rƒ + Ba (E(rm) - rƒ) or E(rarf) = ẞa (E(rm) — rƒ) ⚫ CAPM test regression: Tit-Tft = ai + ẞi(rmt − rft) + Eit Fama French 3-factor model: E(rar): E(SMB)+ha E(HMLt) = - BaE(Tm rf) + Sa * Fama French test regression: Tat - rft = αa + Ba * (Tmt - Tft) + Sa * (SMB)+ha (HMLt) + Eit Carhart 4-factor model: E(rar) = Ba* E(™m - rƒ) + Sa * E(SMBt) + ha * E(HMLt) + maE(MOM) Carhart 4-factor test regression: Tat-Tft = a + Ba* (Tmt − ˜ft) + Sa * (SMB₁) + ha* (HMLt) + ma* (MOM₁) + Eit • mktr ft = rmt-Tft is the excess return on the US stock market. ⚫ SMB₁ = "small,t - "big,t is the return on the portfolio of small-cap US stocks in excess of the return on a portfolio of large-cap US stocks. • HML₁ = Thigh,t-Tlow,t is the return on the portfolio of high book-to- market (value) stocks in excess of the return on the portfolio of low book-to-market (growth) stocks. ⚫ MOM₁ = "Winners,t - "Losers,t is the return on stocks with high returns over the prior 12 months in excess of the return on stocks with low returns over the prior 12 months. ⚫ return = Ending Value-Starting Value Starting Value Price+Div-Price Priceo • Ba= = corr(rm.ra)σ(ra) 0(1b) = Slope of the best fit line through plot of ra vs. Tm
• (1+11/2)2-0.5 (1+12/2)2-2 P CF₁ CF₂ - + + + CFT CF1 CF2 = (1+ytm/2)1-2 (1+ytm/2)2-2 + + (1+r7/2)1-2 CFT (1+ytm/2)1-2 + P= (w1, 1,, Wn) ⇒ Duration: = w₁ D₁+w2 ⋅ D₂+ ... + Wn · Dn AP/P-Durp Ay . •AP/P-Durp Ay + ½ Convexity (Ay)² wo . • ΨΑ = where w = 1+wo(1-BA) αA/02(EA) E(rm-rƒ)/0²(rm)* WM = 1 - WA. • t-statistic = estimate-null value standard error • If t>2, then p-value < 0.05 • P = D₁ = E₁x (1- b) Formulas and facts: ⚫ Accrued interest = (#days since last coupon/number of days per coupon period)*coupon • CAPM: E(ra) = rƒ + Ba (E(rm) - rƒ) or E(rarf) = ẞa (E(rm) — rƒ) ⚫ CAPM test regression: Tit-Tft = ai + ẞi(rmt − rft) + Eit Fama French 3-factor model: E(rar): E(SMB)+ha E(HMLt) = - BaE(Tm rf) + Sa * Fama French test regression: Tat - rft = αa + Ba * (Tmt - Tft) + Sa * (SMB)+ha (HMLt) + Eit Carhart 4-factor model: E(rar) = Ba* E(™m - rƒ) + Sa * E(SMBt) + ha * E(HMLt) + maE(MOM) Carhart 4-factor test regression: Tat-Tft = a + Ba* (Tmt − ˜ft) + Sa * (SMB₁) + ha* (HMLt) + ma* (MOM₁) + Eit • mktr ft = rmt-Tft is the excess return on the US stock market. ⚫ SMB₁ = "small,t - "big,t is the return on the portfolio of small-cap US stocks in excess of the return on a portfolio of large-cap US stocks. • HML₁ = Thigh,t-Tlow,t is the return on the portfolio of high book-to- market (value) stocks in excess of the return on the portfolio of low book-to-market (growth) stocks. ⚫ MOM₁ = "Winners,t - "Losers,t is the return on stocks with high returns over the prior 12 months in excess of the return on stocks with low returns over the prior 12 months. ⚫ return = Ending Value-Starting Value Starting Value Price+Div-Price Priceo • Ba= = corr(rm.ra)σ(ra) 0(1b) = Slope of the best fit line through plot of ra vs. Tm
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
Related questions
Question
1. A hedge fund currently invests in $100 million of mortgage-backed securities (MBS) that have a duration of 15 and convexity of -500 (negative five hundred). Which of the following is closest to how much money the fund would gain or lose if interest rates decreased by 1%, using the duration+convexity approximation?
Group of answer choices
- Lose $12 million
- Lose $10 million
- Lose $12.5 million
- Gain $11 million
- Gain $12 million
2. A hedge fund currently invests in $100 million of mortgage-backed securities (MBS) that have a duration of 15 and convexity of -500 (negative five hundred). Suppose the Hedge fund financed their $100 million of MBS by using seven-day repurchase agreements in addition to their investors’ capital. Assuming they borrow the maximum amount, the required haircut is 10%, and the interest rate is 2% per year, which of the following is closest to how much interest they will owe at the end of the first seven-day term?
Group of answer choices
- $35,000
- $40,000
- $30,000
- $38,000
- None of the above
Transcribed Image Text:•
(1+11/2)2-0.5 (1+12/2)2-2
P
CF₁
CF₂
-
+
+ +
CFT
CF1
CF2
=
(1+ytm/2)1-2 (1+ytm/2)2-2
+ +
(1+r7/2)1-2
CFT
(1+ytm/2)1-2
+
P= (w1,
1,, Wn) ⇒ Duration: = w₁ D₁+w2 ⋅ D₂+ ... + Wn · Dn
AP/P-Durp Ay
.
•AP/P-Durp Ay + ½ Convexity (Ay)²
wo
.
• ΨΑ
=
where w
=
1+wo(1-BA)
αA/02(EA)
E(rm-rƒ)/0²(rm)*
WM = 1 - WA.
• t-statistic =
estimate-null value
standard error
• If t>2, then p-value < 0.05
• P
=
D₁ = E₁x (1- b)
Transcribed Image Text:Formulas and facts:
⚫ Accrued interest = (#days since last coupon/number of days per coupon
period)*coupon
• CAPM: E(ra) = rƒ + Ba (E(rm) - rƒ) or E(rarf) = ẞa (E(rm) — rƒ)
⚫ CAPM test regression: Tit-Tft = ai + ẞi(rmt − rft) + Eit
Fama French 3-factor model: E(rar):
E(SMB)+ha E(HMLt)
=
-
BaE(Tm rf) + Sa *
Fama French test regression: Tat - rft = αa + Ba * (Tmt - Tft) + Sa *
(SMB)+ha (HMLt) + Eit
Carhart 4-factor model:
E(rar) = Ba* E(™m - rƒ) + Sa * E(SMBt) + ha * E(HMLt) +
maE(MOM)
Carhart 4-factor test regression:
Tat-Tft = a + Ba* (Tmt − ˜ft) + Sa * (SMB₁) + ha* (HMLt) + ma*
(MOM₁) + Eit
• mktr ft = rmt-Tft is the excess return on the US stock market.
⚫ SMB₁ = "small,t - "big,t is the return on the portfolio of small-cap US
stocks in excess of the return on a portfolio of large-cap US stocks.
• HML₁ = Thigh,t-Tlow,t is the return on the portfolio of high book-to-
market (value) stocks in excess of the return on the portfolio of low
book-to-market (growth) stocks.
⚫ MOM₁ = "Winners,t - "Losers,t is the return on stocks with high returns
over the prior 12 months in excess of the return on stocks with low
returns over the prior 12 months.
⚫ return = Ending Value-Starting Value
Starting Value
Price+Div-Price
Priceo
• Ba= =
corr(rm.ra)σ(ra)
0(1b)
=
Slope of the best fit line through plot of ra vs. Tm
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