Prices, Discount Factors and Arbitrage / One Factor Risk Metrics and Hedges
About the Lecture
The lecture Prices, Discount Factors and Arbitrage / One Factor Risk Metrics and Hedges by Edu Pristine is from the course Archiv - Financial Markets and Products. It contains the following chapters:
- Day count conventions
- Examples
- Treasury bonds
- One factor Risk Metrics and Hedges - DV01
- Duration based hedging strategies
- Portfolio Duration and Convexity
- Barbell and Bullet Strategy
Author of lecture Prices, Discount Factors and Arbitrage / One Factor Risk Metrics and Hedges
Edu Pristine
Customer reviews
5,0 of 5 stars
| 5 Stars |
|
5 |
| 4 Stars |
|
0 |
| 3 Stars |
|
0 |
| 2 Stars |
|
0 |
| 1 Star |
|
0 |
Excerpts from the accompanying material
... way in which interest is accrued over time. Day count conventions normally used in US are: Actual / actual ...
... is 184 days desired period is Mar 1 and July 3, is 124 days interest earned is 124/184*6 = $4.043 30 / 360 a corporate bond with face value $100 pays a semi-a nnual coupon of 12%. Coupon payment dates are Mar 1 and Sept 1. Find the interest earned between Mar 1 & July 3 ...
... are quoted in dollars and 1/32nd of a dollar $82–27 is equivalent to $82.84375 Cash price / dirty price ...
... delivered the party with the short position, the amount transacted is: Quoted futures price + accrued interest where, quoted futures price = settlement price conversion factor. The conversion factor is equal to the quoted price the bond would pay per dollar ...
... payment of $10 was paid on a treasury bond on June 19, 2009. The next coupon ...
... A time period between June 19 and December 19 is 183 days. Hence the interest the December coupon accrues ...
... party with the short position can chose to deliver the cheapest bond when it comes to delivery, hence he would chose the cheapest to deliver bond net pay out for delivery ( he has to buy a bond and deliver it): Quoted bond price – (settlement ...
... covered in the first part of this presentation: Convexity Price ...
... This reading also covers the following readings from ...
... 1 month, 3 months 6 months and 12 month LIBORs Opportunity cost for AA rated banks Not entirely risk free repo rates and Reverse Repo : Repo rate is the rate at which banks borrow money from the central bank. Reverse Repo rate is the rate at which the central bank borrows money from banks a repurchase agreement (also known as ...
... expressed in the form of another rate. For example an interest rate of 10% compounded semi-annually would fetch (1 + 10% / 2) * (1 + 10% / 2 ) = 1.1025 (remember 6months rate is 10% / 2) on $1 after one year. This ...
... per annum compounded continuously, then what is ...
... a year will become 1.ert = e 0.1x1 = 1.10517. Had it been just annual compounding, ...
... annum compounded semi-annually then what is the ...
... => r = 0.09758 = 9.758% Alternatively, following formulae can be used to ca lculate the interest rates: c= Continuous ...
... ABC promises to repay the money back to X after 5 years and also pay 5% of the $100 principle every year, semi-annual y in the above ...
... at the end of its life b the bond price c coupon payment r zero interest rate at time t bond principal t time to maturity. The yield of a bond is the discount rate (applied to all future cash flows) at which the present value of the bond is equal to its market price yield to Maturity = Investor’s Required Rate of Return the par ...
... 7 7 7 7 Principal payment 100 PV factor 0.892857 0.797193878 0.711780248 0.635518078 0.567427 0. 506631 0.452349 0.403883 0.36061 0.321973 Total PVs 6.25 5.580357143 4.982461735 4.448626549 3.971 988 3.546418 3.166445 2.827183 2.52427 34.45114 Bond price 71.74888 Years 1 2 3 4 5 6 7 8 9 10 Yield 13% Coupon payments 7 7 7 7 ...
... required YTM Liquidity– The less liquid the bond, the higher the required YTM Call features – Increase required YTM a bond that can be redeemed by the issuer prior to its maturity ...
... purchase price bills are sold in increments of $100. The minimum purchase is $100 Boot Strap Method to determine zero rates consider the bond prices of Treasury bonds given be low in column 4. Calculate the continuously compoun ded zero rates for 6 months, 12 months, 18 months and ...
... interest rate, F t1,t2 ,is fixed for a certain principal between times T 1and T 2The payer of the fixed interest rate is also known as the borrower or the buyer. The buyer hedges against the ...
... forward rate of 5%, Actual 90-day LIBOR at settlement is 6% What ...
... Value at the end of agreement = (6% – ...
... payments are made. And the weights are a ratio of the coupon paid at time t to the present bond price Where: t = Respective time period c = Periodic coupon payment y = Periodic yield n = Total no of periods ...
... rates A bond’s interest rate risk is affected by: Yield to maturity term to maturity size of coupon from Macaulay’s equation we get a key relationship: In the case of a continuously compounded yield the duration used is modified duration given as: Consider a ...
... relationship = Note that this is the second partial derivative of the bond valuation equation w.r.t. the yield hence, convexity is the rate of ...
... due to a fall in YTM is greater than the price decline due to a rise in YTM, given an identical change in the YTM for a given change in YTM, bond prices will ...
... by using duration and convexity: ()()() ...
... Question 23 if yields rise by 1% per ...
... + = ? ! "#$ $ # % "#$ ...
... the geometric mean of expected future short interest rates liquidity preference theory investors must be paid a “liquidity premium” to hold less liquid, long-term debt market segmentation theory investors decide in advance whether they want to invest in short term or the long term ...
... upward sloping: This is the most persistent shape historically when short-term interest rates and inflation are low downward sloping ( declining): This occurs at peaks in the short-term interest rate cycle, when inflation is expected to decrease in the future flat: This shape is evident during periods ...
... Classes Risk Premiums (Yield Spreads) 27 Percent Term Left to Maturity 16 14 12 10 ...
... curve below and the economic impacts ...
... of a $100 bond when the zero rates (Continuous Compounded) on months, 12 months and 18 months are 4%, 4.5% and ...
... treasury bonds 30 / 360 corporate bonds actual/360 money market instruments. The interest earned between two dates (number of ...
... dollar interest is $100*0.09*91/360 = $2.275 rate of interest = 2.275/(100-2.275) = 2.328 % Actual / Actual a treasury bond with face value $100 pays a semi-an nual coupon of 12%. Coupon payment dates are Mar 1 and Sept 1. Find the interest earned between Mar 1 & July 3 reference period Mar 1 to Sept ...
... the price at which the investor buys a bond from the market cash price = quoted price + accrued ...
... bond futures contract expires, any govern ment bond with maturity more than 15 years on the first day of the delivery month and is not callable for the next 15 years from that day can be delivered conversion price when a bond ...
... due on December 19, 2009 and we are currently on September 1, 2009. If the ...
... the December coupon has accrued interest is the time period between June 19 to September 1 (74 days). The actua ...
... price * conversion factor) consider an example in the table below where the short position holder has 3 options for delivery. His cheapest to deliver bond is bond 2 cheapest to deliver bond (All figures in $) settlement future price: 94.23 bond quoted bond price conversion factor 1 ...
... or dollar value of basis point (DV01) change is the absolute change in the bond price from one basis point change in yield. ...
... contract in such cases the number of contracts to hedge is given by the e quation below: f C Contract price for interest rate futures d F Duration of asset underlying futures at maturity p Value of portfolio being hedged d ...
... duration of the portfolio of government bonds at the end of 6 months is 7.1 years. The duration of the cheapest to deliver T-bond in December is given as 9.121 years. What position should the investor take ...
... 43 the number of contracts that should be shorted is: ...
... the weighted sum of durations of individual securities negative convexity callable bonds exhibit negative convexity when yields fall below certain level at lower yield, there is incentive for the issuer ...
... barbell strategy, investor uses the bonds of short and long maturities and does not invest in ...
... yield of a $100 bond when the zero rates (Continuous Compounded) on 6 months, 12 months and 18 months are 4%, 4.5% ...
... 30/360 corporate bonds, actual/360 money market instruments. The interest earned between two dates (Number ...
... Dollar interest is $100*0.09*91/360 = $2.275; Rate of interest = 2.275/(100-2.275) = 2.328 % Actual. A treasury bond with face value $100 pays a semi-annual coupon of 12%. Coupon payment dates are Mar 1 and Sept 1. Find the interest earned between Mar 1 & July 3; Reference period Mar 1 to Sept ...
... is the price at which the investor buys a bond from the market; Cash price = Quoted price + accrued ...
... Treasury bond futures contract expires, any government bond with maturity more than 15 years on the first day of the delivery month and is not callable for the next 15 years from that day can be delivered. Conversion price: When a bond ...
... is due on December 19, 2009 and we are currently on September 1, 2009. If ...
... which the December coupon has accrued interest is the time period between June 19 to September 1 (74 days). The ...
... Consider an example in the table below where the short position holder has 3 options for delivery. His cheapest to deliver bond is Bond 2. Cheapest to Deliver Bond (All figures in $), Settlement Future Price: 94.23 Bond, Quoted Bond Price Conversion Factor ...
... or dollar value of basis point (DV01) change is the absolute change in the bond price from one basis point change in yield. ...
... In such cases the number of contracts to hedge is given by the equation below: FC Contract price for interest rate futures, DF Duration of asset underlying futures at maturity, P Value of portfolio being hedged ...
... the duration of the portfolio of government bonds at the end of 6 months is 7.1 years. The duration of the cheapest to deliver T-bond in December is given as 9.121 years. What position should the investor ...
... The number of contracts that should be shortened is: ...
... the weighted sum of durations of individual securities. Negative Convexity Callable bonds exhibit negative convexity when yields fall below certain level. At lower yield, there is incentive for the issuer ...
