1.01.2005

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» Q&A: What are the coupon payments for a $50,000 par value...
» Q&A: List some duties of the trustee appointed...
» Q&A: What are some of the more common coupon rate structures?
» Q&A: What's the difference between a non-callable bond...
» Q&A: If an investor believes that yield curve will flatten...
» Q&A: Why is it important to recognize the options embedded...
» Q&A: If an investor needs to borrow funds for bonds purchase...
» Q&A: How is a regular redemption price different from...
» Q&A: What's the reinvestment income of...
» Q&A: What's the yield-to-first-call of...

Q&A: What are the coupon payments for a $50,000 par value...

...8% coupon rate, monthly-pay, mortgage-backed security?

Answer : $50,000 * 8% / 12 = 333.33

  • With monthly coupon payments, the annual coupon rate is divided by 12 to determine the monthly coupon rate.

Bonus Points

  • Although bond coupon rates are usually stated in annual rates, the actual coupon is divided into two semi-annual payments.
  • The par value for most corporate bonds is $1,000, higher denominations for government issues.
    • The bond's final cashflow includes the return of par value.
  • Bonds which are unsecured obligations of the company are called debentures.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: List some duties of the trustee appointed...

...when bonds are issued?

Answer

  • Make sure terms of the indenture are obeyed
  • Manage the sinking fund
  • Monitor the protective covenants for the bondholders
  • Represent the bondholders in default

Bonus Points

  • A bond indenture is made out to a third-party trustee as bondholders may have difficulty in ascertaining whether the issuer has been fulfilling its obligations.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: What are some of the more common coupon rate structures?

Answer
  • Zero-coupon bonds: pay the face amount at a future maturity date, without any interim interest payments. ie. a zero-coupon bond with $1,000 par is quoted at 80. The interest is $200. A type of accrual bonds that do not make any coupon payments until the maturity date.
  • Step-up bonds: have low initial and gradually increasing coupon rates, (ie. rates "step up" over time). eg. A 5-year, annual-pay, step-up bond with scheduled coupon rates of 4%, 5% and 6%.
  • Deferred coupon bonds: no coupon payments for an initial period of typically 3 - 7 years. Then a lump-sum coupon is paid, and regular coupon payments begin. eg. an annual-pay deferred coupon bond with 3-year deferral period, 10 years to maturity, 10% coupon rate and $1,000 par value. Its cashflows are $0 for years 1-2, $264.80 year 3 (FV with 8% rate), $100 years 4-9, $1,100 year 10.

Bonus Points

  • Coupon rate is the interest rate that the issuer agrees to pay each year.
    • typically pay semiannually.
    • The amount of interest that will be received by the buyer if an investor sells a bond between coupon payments (as interest is paid not daily) is known as accrued interest. The agreed upon bond price without accrued interest is referred to as the price (clean price). Full price or dirty price otherwise.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: What's the difference between a non-callable bond...

... and a non-refundable bond?

Answer : Non-refundable prevents redemption only from certain sources, namely the proceeds of other debt issues sold at a lower cost of money (ie. when interest rates decline). A non-refundable bond can be callable if cash flows are from other sources, such as operations, common stock sale, or sale of property.

Non-callable is much more absolute than refunding protection - it has complete protection against early retirement.

Bonus Points

Provisions for paying off bonds

  • A call provision is the right of the issuer (not obligation) to retire the issue prior to the stated maturity date.
    • Bonds can be called in whole or in part.
    • Typically, call provisions have a deferment period (ie. the issuer may not call the bond for a number of years until a specified first call date is reached)
    • Typically, a call schedule specifies a number of call dates, and sets a call price for each call date. The call price at the first call date generally has a premium over the par value.
    • Call provision gives the corporation the option to force retirement of the entire debt issue prior to maturity, whereas a put provision gives the bondholder the same option. (put valuable if interest rates have gone up and bond prices have gone down.)
  • A refunding provision permits the issuer to redeem bonds using proceeds from issuing lower cost debt obligations ranking equal to or SUPERIOR to the original debt.
  • A prepayment option allows principal repayment prior to the scheduled data (ie. a prepayment). Typically the price at which a loan is prepaid is par value. Commonly used in amortizing securities that are backed by loans (e.g. mortgage and car loans).
  • A sinking fund provision allows to retire a specified portion of the bond each year to reduce credit risk. The issuer can fulfill the requirement by
    • Making a cash payment of the required sinking fund to the trustee, who then retires the bonds using a lottery; or
    • Purchase bonds in the open market, and deliver them to the trustee.
  • Index amortizing notes: principal repayments are made prior to the started maturity date based on the prevailing value for some reference rate. The principal payments are structured to accelerate when the reference rate is low.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: If an investor believes that yield curve will flatten...

...what could he do to benefit from it?

Answer : He could short sell 2-year treasury bond and purchase 10-year treasury bond, for instance.

  • Flatten yields mean long term yields decrease relative to short term yields, thus the opposite price movements (price of long term bonds increase relative to short term)
  • If a decline in rates is expected, bonds prices move up.

Bonus Points

  • Normally the yield curve is upwards sloping. It means that longest bonds have highest YTM than shortest have.
  • Steepen yields mean long term yields increase relative to short term yields, thus the opposite price movements

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: Why is it important to recognize the options embedded...

...in a bond?

Answer : A bond may have more than one embedded option, and these options have a direct effect on the value of a bond, as well as the performance of a bond measured by the rate of return. They affect both the timing and the level of the future cash flows from the bond.

  • When the interest rates fall, call/prepayment/accelerated sinking fund provision options become more valuable to the bond issuer (and floor on a floater more valuable to the bond holder.) For example, the issuer can retire the bond paying high coupon rate, and replace it with lower coupon bonds (although call provisions are detrimental to the bondholders as the proceeds can only be reinvested at a lower interest rate.)
  • Because of the embedded options, it is necessary to develop models of interest rate movements and rules for exercising these options. Such models are typically based on a number of assumptions. Investors are exposed to the risk that the valuation models may produce the wrong value due to incorrect assumptions (aka model risk.)

Bonus Points

  • An embedded option is a provision in the bond indenture that gives the issuer and/or the bondholder an option to take some action against the other party.
  • An embedded option benefits the issuer if it gives the issuer a right or it puts an upper limit on the issuer's obligations.
    • call option: the right to call the issue back at some pre-determined price level.
    • prepayment option: the right of the underlying borrowers in a pool of loans to prepay an amount in excess of the scheduled principals repayment.
    • accelerated sinking fund provision: the issuer can call more than is necessary to meet the sinking fund requirement when interest rates decline.
    • the cap of a floater: it requires no action by the issuer to take advantage of a rise in interest rates.
  • An embedded option benefits the bondholder if it gives the bondholder a right or it puts an lower limit on the bondholder's benefit.
    • conversion option: a convertible bond is an issue that grants the bondholder the right to convert the bond for a specified number of shares of common stock. The feature allows the bondholder to take advantage of favorable movements in the price of the issuer's common stock.
      • The yield on the convertible will typically be higher than the yield on the underlying common stock.
      • The convertible bond will likely participate in a major upward movement in the price of the underlying common stock.
      • A convertible bond can be valued as a straight bond with an attached option.
    • put option: it grants the bondholder the right to sell the issue back to the issuer at a specified price (called put price) on designated dates.
    • floor on a floater: it benefits the bondholder if interest rates fall.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: If an investor needs to borrow funds for bonds purchase...

...what are some of the more common sources he can turn to?

Answer

  • Margin Buying: The funds are provided by the broker, and the broker gets the money from a bank using the same underlying bond as collateral.
    • The bank charges the broker an interest rate (known as call money rate, or broker loan rate), and the broker charges the investor the call money rate plus a service charge.
  • Repurchase Agreement: It is the sale of a security with a commitment by the seller to buy the same security back from the purchaser at a specified price at a designated future date. It is actually a collateralized loan.
    • The difference between the purchase (repurchase) price and the sale price is the dollar interest cost of the loan. The implied interest rate is called the repo rate.
    • A loan for 1 day is called an overnight repo. A loan for more than 1 day is called a term repo.
    • When a non-dealer uses the repo market to borrow funds, it is called a reverse repurchase transaction; when a dealer uses the repo market to borrow funds it is called a repurchase transaction.

Bonus Points

  • Margin Buying is the most common collateralized borrowing arrangement for common stock but not the common borrowing vehicle for institutional bond investors.
    • In the US, the percentage of a bond's value that can be bought on margin is regulated by the Federal Reserve.
  • The repo rate is lower than the cost of bank financing, but credit risks are faced by both parties. It is like a forward market without a clearinghouse.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: How is a regular redemption price different from...

...a special redemption price?

Answer : A regular redemption price is the normal call price for a typical callable bond (after the first call date). It is usually above par until the first par call date.

Special redemption prices are for bonds redeemed from through the sinking fund and through other provisions, and the proceeds from the confiscation of property (through the right of eminent domain or the forced sale or transfer of assets due to deregulation.) A special redemption price is usually par value.

Category: C++ Quant > Finance > Debt

Your Turn!

 

Q&A: What's the reinvestment income of...

...the 2nd coupon payment of a 5-year, 8% $100 par bond when the reinvestment rate is 10%?

Answer : coupon FV - par = FV - 100*8%/2 = 5.9-4 = $1.9

  • With Excel FV function, Nper=8, Rate=10/2%,PV=100*8%/2, one gets FV=5.9

Category: C++ Quant > Finance > Debt > Valuation

Your Turn!

 

Q&A: What's the yield-to-first-call of...

...a 8-year, 6%, $100 par bond selling for $104.50, if the first call date is in 3 years with a call price of $102?

Answer : With Excel Rate function, Nper=6, PV=-104.5, PMT = 6/2 = 3.5, FV=102, rate=2.5%. Annualize it and one gets 5%.

Category: C++ Quant > Finance > Debt > Valuation

Your Turn!