How Sinking Funds Change Bond Cash Flows, Risk, and Valuation

# Valuation of a Sinking Bond Fund


# Valuation of a Sinking Bond Fund












What would the schedule of payments be for a bond with a sinking fund? I know how to price a bond but how does the sinking fund play into it?

```
Semi-Annual Pay Bonds   
Maturity    12/31/2033
Original Par    10,000,000
Coupon Rate 4%
First interest payment date 6/30/2014

Principal Sinking Fund payments of $1 million per year  
(in December) for last 10 years starting in 12/31/2024  
(through 12/31/2033)    

              Bond Interest Payment    Bond Principal Payment   Total Bond Payment
6/30/2014           
12/31/2014          
6/30/2015           
12/31/2015          
6/30/2016           
12/31/2016          
6/30/2017           
12/31/2017          
6/30/2018           
12/31/2018          
6/30/2019
```

## Answer by jeff m (score 2, accepted)

https://quant.stackexchange.com/a/8537

A sinking fund provides credit enhancement for the investor and reduces interest rate risk for the issuer. The obligor will purchase a pre-determined amount of bonds to be retired in the open market if they're trading below par, or they will make payments to the appointed trustee who will buy-back the bonds in a lottery(typically at a pre-determined call price). Schedules vary considerably and may include other provisions such as deferment periods or acceleration features. One just needs to read the indenture to see how predictable the schedule will be.

From the investors point of view, the advantages of a sinking fund is that it ensures a timely paydown of the principal so the maturity payment is easier to make. It will enhance the liquidity of the debt, which is especially nice for smaller issues in thinner secondary markets. Finally, the pricing will be more stable since the issuer may become an active participant in the buy side when prices fall. All of these will nudge the bond towards lower yields and tighter spreads.

There are some drawbacks, especially if you happen to be one of the lottery bonds called early, wasting your time in analyzing the bond and potentially relinquishing a high coupon if rates fall. This can put downward pressure on new issues prices when interest rates are high since contraction risk will be greater. Other features such as acceleration can also put downward pressure on prices.

As for actually pricing the bond, treat it as you would a callable bond. The indenture, or preferably your data provider, will give you the information you need. Besides the obvious coupon/frequency etc., you need to know the probability of it being retired(amount to retire/remaining issue size), the price you will receive if retired, and the corresponding schedule.

## Answer by PBD10017 (score 2)

https://quant.stackexchange.com/a/8558

I assume the sinking fund is optional and non-cumulative. In effect the issuer of the bond holds 10 European call options on 1 million at 4% each. These are valued using a binomial tree and are interest rate dependent. To value the bond price the bond as if there were no options embedded (I.e. it's single bullet, plain vanilla bond) and then add (really subtract) the value of the options.

I assume that every year the issuer can call a maximum of 1 million. If they are cumulative (e.g. if in year 2 the issuer can call 2 million if a million was not called the year before) then you're best left off with a monte-carlo simulation.

Fixed Income Securities and Derivatives Handbook - Choudry. Binomial trees starting point: http://en.wikipedia.org/wiki/Binomial_options_pricing_model