# Bond Pricing and Trade Premium

# Bond Pricing and Trade Premium

Trade premium is a topic that all mortgagors ought to be familiar with - certainly their fellow mortgagees are. Understanding trade premiums will help you better understand where interest rates come from and why they might change.

Furthermore, trade premium can be a terrific tool for borrowers. Some loan programs, such as the HUD 223(a)(7), allow the cash from trade premiums to be used to pay prepayment penalties. Many lenders will negotiate lowering their upfront fees in return for increased trade premium.

So let’s walk through an example, step by step.

## Calculating Bond Price

A bond, `Bond A`

, for $15M is issued with a 35 year, fully-amortizing term and a monthly coupon payment of $50,000 (~2% rate). Let’s assume it is prepayable in year 10 without penalty. These terms are fixed for the life of the bond.

At the same time as the above bond is issued, another similar $15M bond is issued, `Bond B`

, with the same risk profile, 35 year term and prepayment schedule. However, this bond feature a monthly payment of $53,000 (~2.4% rate) - $3,000 more than the first bond.

Bond A | Bond B | |
---|---|---|

Principle | $15M | $15M |

Amortization Term | 35yr | 35yr |

Rate | ~2.04% | ~2.42% |

Monthly Payments |
$50,000 |
$53,000 |

If both `Bond A`

& `Bond B`

are offered to the market on the same day, `Bond B`

should fetch a larger price than `Bond A`

. How much of a higher price `Bond B`

will fetch is the important point for us to consider.

Bond pricing is the simple function of how much money, over what period and at what risk an investor can expect to receive. Let’s discuss each of these three components:

### How Much Money: The Interest Rate & Amortization Term

A bond’s cashflow is it’s monthly principle and interest payments (P&I) (and balloon payment, ultimately). Two factors come to play with P&I, the interest rate as well as the amortization term. The principle portion goes up *the shorter the term*, since your payments are spread out over fewer months.

The interest portion goes up, of course, with a higher interest rate.

It’s clear that, if we assume all else is equal between `Bond A`

and `Bond B`

, `Bond B`

delivers more cash to investors throughout its term, and will therefore be priced higher than `Bond A`

. Specifically, `Bond B`

delivers $3,000 more per month.

**Both interest rate and amortization term make up the monthly coupon amount.**

### Over What Period: The Prepay Schedule

`Bond B`

pays $3,000 more per month - now we turn to the question of how long will these payments last. The first place to look is the bond’s loan term. This is the maximum length the bond will remain outstanding.

The second place to look is the prepayment schedule. Many bonds can be prepaid early, typically with a penalty fee. Investors try to anticipate the likeliness of an early prepayment, since this affects how much they expect to make over the term of the bond.

In our example both `Bond A`

and `Bond B`

have zero prepayment penalty after year 10. So let’s assume that we think both bonds will be prepaid after 10 years. In this case, `Bond B`

will deliver $360,000 more than `Bond A`

:

**The loan term and prepayment schedule affect how long the bond will remain outstanding, and therefore how much in total an investor will make on the bond.**

### At What Risk: The Discount Rate

So we’ve established `Bond B`

will make $360,000 more over ten years. Our last question is, how much more would an investor pay today to receive the additional $360,000 over ten years. As we know from Finance 101, this is simply calculating the present value of an annuity:

We already know the `Coupon`

and we know `t`

, the term of the annuity. `r`

, the discount rate, is what is left to discuss. You might be tempted to assume the discount rate is our bond’s interest rate, but this is not quite so. The interest rate was included in our coupon payment. Let’s look at discount rates more closely.

Let’s just focus on the $360,000 for a moment. You and I probably have somewhat different plans for the next 10 years. Let’s assume you’re a responsible investor, and you are willing to put aside money today for a moderate gain over the next 10 years. I, on the other hand, am trying my hand at a startup and really prefer having cash today instead of in a few years from now.

If you came across the opportunity to make $360,000 over the next ten years, and the opportunity had almost zero risk (since it is with government insured securities) - how much would you pay today? Let’s assume in your current bond portfolio, you average a 5% return, and you’d like to maintain that rate:

I, on the other hand, would really prefer my cash today, and you’d have to offer me a much larger return for me to forego cash today. Say I would require a 25% return to consider parting with cash, I would pay:

Every investor has their own discount rate in mind, which is a function of their current situation and the alternatives available. In large, liquid bond markets, the *market discount rate* is effectively the collection of many investors, like us, bidding bonds up and down, based on our own needs for capital return (yield).

### Putting It All Together: The Bond Price

Now let’s plug this back in to our `Bond A`

vs `Bond B`

analysis.

Let’s assume the market discount rate is 2% for these sorts of bonds. Let’s also assume that investors will assume these bonds will prepay after 10 years. Let’s price them:

**Bond A**

There are two components to price, the coupon payments for the 10 year period, followed by the balloon payment of the leftover principle.

*Coupon value*

*Future Balloon Payment*

**The principle balance after 10 years is $11,742,113*.

*Total Price*

In short, an investor would pay $15M today to own this $15M Bond. This makes intuitive since, since the interest rate on the bond is identical to the discount rate.

In bond terms, the bond price would be **100**:

**100 is also called par*

**Bond B**

*Coupon value*

*Future Balloon Payment*

**The principle balance after 10 years is $11,918,053*.

*Total Price*

*Bond Price*

Bond A | Bond B | |
---|---|---|

Coupon | $50,000 | $53,000 |

Value | $15M | $15.47M |

Bond Price |
100 |
103 |

## Bond Prices and Trade Premium

Many mortgagees sell the mortgages to investors. The price they receive less the amount they lent is the trade premium.

In terms of our example, `Bond A`

was a $15M loan that sold for $15M. The lender doesn’t make any additional money on the sale of that loan (excluding any direct fees the borrower pays). This is a “par trade”.

`Bond B`

, however, gets sold for $15,469,235, which is a net gain to the lender of $469,235 - or ~3% (hence, 103).

**Bond B, with a 0.38% higher rate, sold for a 3% trade premium over bond A**.

## Final Thoughts

The above examples were overly simplified for explanation. The actual market is more messy. For instance, in our example, every increase in rate of should increase the trade premium by another 1%, however you often find that this amount changes.

For example, look at the following schedule of GNMA bonds:

Rate | Approximate Bond Price* | bps change |
---|---|---|

2.20% | 101 | - |

2.22% | 102 | 2bps |

2.25% | 103 | 3bps |

2.29% | 104 | 4bps |

2.37% | 105 | 8bps |

2.50% | 106 | 13bps |

**Approximate GNMA bond prices as of 8/2020*

As you can see, recent GNMA bonds not only have lower rates, the premium concavity is different. Why this happens will be the subject of the next article.