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CFA Level 1 question 90
The price yield relationship curve of the bond for prices above the callable price
a) Will have higher convexity compared to an option free bond
b) Will have negative convexity
c) Will have similar convexity as an option free bond
Ans B: Convexity is the second derivative of price change for a unit change in yield. For a large change in yields one need to do convexity adjustment to get a better approximation of price change of the bond.
For a callable bond when the market price are above the callable price the bond faces the risk of being called and hence for further drop in yield the bond price will not make big moves. At this point the convexity of the bond will turn negative.
CFA Level 1 question 91
The current treasury spot rates for various maturities are given below
0.5 Years – 3%
1.0 years – 3.1%
1.5 years -3.25%
2.0 years – 3.3%
The arbitrage free price of a semi annual coupon paying treasury bond with coupon rate of 7% p.a, face value of USD 100 and exactly 1.5 years left to maturity will be closest to.
a) USD 105.4470
b) USD 105.4563
c) USD 105.4593
CFA Level 1 question 91
The current treasury spot rates for various maturities are given below
0.5 Years – 3%
1.0 years – 3.1%
1.5 years -3.25%
2.0 years – 3.3%
The arbitrage free price of a semi annual coupon paying treasury bond with coupon rate of 7% p.a, face value of USD 100 and exactly 1.5 years left to maturity will be closest to.
a) USD 105.4470
b) USD 105.4563
c) USD 105.4593
Ans B: In an arbitrage valuation all coupons need to be discounted by respective treasury spot rates.
The discount rate should be converted to semi annual rates i.e for 0.5 year it would be 3.0%/2 and so on.
Arb free price = 3/(1+1.5%)^1 + 3/(1+1.55%)^2+ 103/(1+1.625%)^3=USD 105.4563
CFA Level 1 question 92
A bond which pays a coupon of 5.5% pa is trading at a price of USD 102. The bond pays coupon semiannually, has a face value of USD 100 and has 3 years left for maturity. If the Macaulay duration of this bond is 2.80 years then for a 25 bps increase in yield the price of the bond would
a) Decrease to USD 101.27
b) Decrease to USD 101.30
c) Decrease to USD 101.22
Ans B: Duration – In general indicates price sensitivity of the bond's price to change in yields. In specific
Macaulay Duration: Indicates the time taken to get the invested capital back. Faster you get better it is. So, lesser the yield lesser the time required to get your money back and vice versa. However this still does not provide the exact quantum of risk w.r.t yield change.
Macaulay duration will be given by:( t1*PVCF1+t2*PVCF2+…….+ tn * PVCFn)/ (k*Price of the bond)
Where t1, t2 etc represent each cash flow i.e either coupon or principle repayment, PVCFn – indicates Present value of cash flow n and k indicates number of coupon per year.
Modified duration: Modified duration provides the likely percentage change in price of a bond for a percentage change in yield. In other words a modified duration of 4.2 would indicated for every 100 bps change in yield price would approximately change by 4.2% (note the word approximately as for large changes this relationship will not hold good, effect of convexity will come in to play)
Modified duration will be given by = Macaulay duration/(1+[yield/k])
For our question we need Modified duration to find the price change. For which we need to find the yield of the bond. The yield of this bond can be found as 4.78%.
Modified duration = 2.8/(1+[4.78%/2]) = 2.73. This indicates for every 100 bps change in yield price will change by 2.73%.
So for 25 bps change the price change will be approximately 2.73/4 = 0.68.
The price of 102 will decrease by 0.68% i.e 102*0.68= 0.70
Price of the bond after increase in yield will be equal to 102 - 0.69 = USD 101.3
CFA Level 1 question 93
Adam purchased a 5 years semiannual floater bond at a price of $101.23. The face value of the bond is $100 and the coupon is LIBOR+40 bps. The spread for life of this bond is closest to
a) 15.21 bps
b) 15.40 bps
c) 63.82 bps
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CFA Level 1 question 93
Adam purchased a 5 years semiannual floater bond at a price of $101.23. The face value of the bond is $100 and the coupon is LIBOR+40 bps. The spread for life of this bond is closest to
a) 15.21 bps
b) 15.40 bps
c) 63.82 bps
Ans A: The spread for life essentially indicates the average spread that an investor will receive above the reference rate if he holds the bond till maturity. i.e
Let us say currently a bond with 5 years left to maturity which pays a coupon of LIBOR+20 bps is trading at a discount of 100 bps to the par rate.
Now this 100 bps spread will be spread over 5 years, indicating 20 bps/year. The standard spread over LIBOR is 20 bps/year. So a total spread of 20+20 =40 bps. However please note this spread is correct only if you buy the bond at par value, to adjust the spread for your actual purchasing price multiply the above spread for life by [ face vale / Purchase price]
This does not take Time value in to account which is one of the disadvantage of this measure.
The spread for life can be calculated as (Note the spread will be always measured in basis points)
SFL = { [100 * (100-Price)]/ Life of the bond + Spread above reference rate} * 100/ Price of bond
{[100*(100-101.23) / 5] + 40} * 100/ 101.23}
= (-24.6+40)* 100/101.23 = 15.21 bps
CFA Level 1 question 94
A Zero coupon bond with exactly four years left for maturity is trading at USD 77.52. The face value of this bond is USD 100. The Yield to Maturity of this bond is closest to
a) 6.67%
b) 6.57%
c) 6.47%
CFA Level 1 question 94
A Zero coupon bond with exactly four years left for maturity is trading at USD 77.52. The face value of this bond is USD 100. The Yield to Maturity of this bond is closest to
a) 6.67%
b) 6.57%
c) 6.47%
Ans C: While many of us felt that this is an easy and straight forward question, some of us missed the important point.
€œIn the absence of coupon all bonds are considered as semi annual coupon paying bonds.(refer page 457 book 5). €œ
For our question this would imply
100/(1+r)^8 = 77.52. And the yield on bond is r*2. I.e 100 discounted by semiannual yield for eight period (8 semi annual coupon paying periods). Solving for 'r' we would could 3.234% which is semiannual yield. The annual yield would be 3.234*2 = 6.47%
CFA Level 1 question 95
A 5 year annual coupon paying bond is trading at a price of USD 102.19. The duration of the bond is 4.35 and convexity of the bond is 0.24. For a 200 bps increase in yield the price of the bond will approximately move to
a) USD 93.79
b) USD 93.30
c) USD 92.80
CFA Level 1 question 95
A 5 year annual coupon paying bond is trading at a price of USD 102.19. The duration of the bond is 4.35 and convexity of the bond is 0.24. For a 200 bps increase in yield the price of the bond will approximately move to
a) USD 93.79
b) USD 93.30
c) USD 92.80
Ans B: The modified duration gives price change of a bond only for a small movement in yield. For larger changes one need to do convexity adjustment. So, for large movement in yields price changes should be estimated by
Duration * Change in yield in percentage + 0.5 * Convexity * (change in yield )^2
-4.35*.02 + 0.5*0.24 *(.02)^2 = -8.7%
The price of USD 102.19 will decrease by 8.7% i.e 102.19*(1-8.7%) = 93.30
CFA Level 1 question 96
Eva purchased Treasury Inflation protected securities (TIPS) on 1-January-2011. The annualized inflation at that time is 2.4% and after six months the same has increased to 2.8%. The TIPS has a face value of $100,000 and coupon of 3.5% p.a paid semiannually. The coupon that will be received by Eva FOR the 2nd half (2nd half ONLY) of the year will be closest to
a. USD 1,750.0
b. USD 1,842.2
c. USD 1,795.8
CFA Level 1 question 96
Eva purchased Treasury Inflation protected securities (TIPS) on 1-January-2011. The annualized inflation at that time is 2.4% and after six months the same has increased to 2.8%. The TIPS has a face value of $100,000 and coupon of 3.5% p.a paid semiannually. The coupon that will be received by Eva FOR the 2nd half (2nd half ONLY) of the year will be closest to
a. USD 1,750.0
b. USD 1,842.2
c. USD 1,795.8
Ans C: The principle for the first half would be 100,000 *(1+1.2%) = 101,200 (1.2% is.half of full year inflation of 2.4%)
Principle for the 2nd half would be 101,200*(1+1.4%)=102.616.8
Interest = 102,616.8 * 3.5%/2 = 1,795.8
CFA Level 1 question 97
John and Sidebottom were discussing about index weighting methodologies
John: The major disadvantage of equal weighted index is the weight of the stock in the index decreases during stock split. The market cap weighted suffers from a disadvantage of being unduly influence by big companies.
Sidebottom: It is easy for an Exchange Traded Fund (ETF) passively tracking a price index to outperform as ETFs receive dividends. The Market cap weighted index need to be re balanced frequently as market cap change every day.
a) Both are Wrong
b) John is right
c) Sidebottom is right
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CFA Level 1 question 97
John and Sidebottom were discussing about index weighting methodologies
John: The major disadvantage of equal weighted index is the weight of the stock in the index decreases during stock split. The market cap weighted suffers from a disadvantage of being unduly influence by big companies.
Sidebottom: It is easy for an Exchange Traded Fund (ETF) passively tracking a price index to outperform as ETFs receive dividends. The Market cap weighted index need to be re balanced frequently as market cap change every day.
a) Both are Wrong
b) John is right
c) Sidebottom is right
Ans A: The equal weight index will not be affected by stock split. It suffers from the disadvantage of requirement for frequent rebalancing. Market cap weighted index adjusts for weighting automatically it need not be rebalanced. Other statements are correct
CFA Level 1 question 98
Which of the below incidents will lead to fall in market efficiency
a) American government banned short selling to avoid market fall after bankruptcy of Lehman brothers
b) Indian Government mandated the listed companies to disclose their Balance sheet at least once in six months compared to earlier limit of at least once in a year.
c) Chinese Government increased the limit for Foreign holding in their listed domestic companies.
