IFT Notes for Level I CFA^{®} Program

A mortgage loan is a loan secured by the collateral of some specified real estate property which obliges the borrower to make a predetermined series of payments to the lender. In simple words, it is a loan a buyer takes for buying a real estate property (land, apartment, house, etc.); the collateral is the property being bought. If the buyer defaults on mortgage payments, then it gives the lender the right to foreclose on the loan, take possession of the property, and sell it to recover funds given as debt.

The cash flow of a mortgage consists of the following three components:

- Interest
- Scheduled principal payments
- Prepayments (any principal repaid in excess of the scheduled principal)

The amount lent as loan towards the purchase of the property is always less than the purchase price. It is equal to the purchase price minus the down payment made by the buyer. The buyer’s initial equity is equal to the down payment made.

The ratio of the mortgage loan amount to the property’s purchase price is called the __loan-to-value (LTV) ratio__**. **

We will now look at the following characteristics of residential mortgage loans in detail:

- Maturity
- Mortgage rate
- Amortization schedule
- Prepayments and prepayment penalties
- Rights of the lender in a foreclosure

Maturity: term of a mortgage is the number of years to maturity. It varies from one country to the other. For example, in the United States it ranges from 15 to 30 years.

The interest rate on the mortgage loan is called the __mortgage rate__ or __contract rate__. How the mortgage rate is calculated varies across countries.

The four basic methods for calculating mortgage rate are:

- Fixed rate: The rate remains fixed during the life of the mortgage.
- Adjustable or variable rate: The adjustable-rate mortgage (ARM) is like a floating rate. Here, the mortgage rate is reset periodically based on some reference rate or index.
- Initial period fixed rate: The mortgage rate is fixed for some initial period and then it is adjusted for either a new fixed rate or variable rate. If the mortgage rate is fixed for an initial period and then set to a new fixed rate, then it is called
__rollover or renegotiable mortgage__. If the mortgage rate is fixed for an initial period and then it becomes adjustable, then it is called a hybrid mortgage. - Convertible: The mortgage is initially either a fixed or an adjustable rate. Later, the borrower may either convert it into a fixed or adjustable mortgage for the remainder of the mortgage’s life.

Residential mortgages are usually amortizing loans. The amount borrowed reduces gradually over time as periodic mortgage payments are made. Mortgage payments consist of interest payments and scheduled principal repayments. Let’s take the example of the Smiths who borrow $100,000 to purchase a house, assume the terms of the loan are as follows:

Loan amount = $100,000; mortgage rate = 6%; maturity term = 30 years.

The periodic mortgage payment can be computed as:

PV = -100,000; N = 360 (=12 * 30); I = 0.5 = (6 / 12); FV = 0; CPT PMT

PMT = -599.95

Interest = 0.005 * 100,000 = $500. But, the monthly payment is $599.95. During the first month, $99.95 goes towards reduction of principal. As time goes by, the amount of the monthly mortgage payment towards principal reduction increases and that toward interest decreases.

Since the outstanding mortgage balance of $100,000 reduces over time, it is called amortization.

There are two types of amortizing loans:

__Fully amortizing loans__: There is no outstanding balance at the end of the mortgage’s life. The loan is fully repaid with the last mortgage payment.__Partially amortizing loans__: The sum of all the scheduled mortgage repayments is less than borrowed amount. A last payment, called the balloon payment, is made equal to the unpaid mortgage balance.

Based on interest/scheduled principal repayments, there are two types of mortgages:

__Interest-only mortgage__: No scheduled principal repayment for a certain number of years.__Bullet mortgage__: No scheduled principal repayment over the entire life of the loan. The last payment is equal to the original loan amount.

Prepayment is a payment made in excess of the scheduled principal repayment. Assume 10 months after taking the loan, the interest rates fall. The Smiths choose to refinance by taking a new loan and closing the existing one by prepaying. Another scenario is part prepayment, where, let us say, in the first month the Smiths pay $1,000 instead of the scheduled $599.95 mortgage payment. $1,000 is broken down into three parts: $500 towards interest, $99.95 for scheduled principal payment, and $400.05 towards prepayment.

In some countries, there may be a penalty for prepayment as it hurts the lender (recall ‘prepayment risk’). The objective of imposing a penalty is to compensate the lender for the difference in the contract rate and the prevailing mortgage rate when the borrower prepays as rates decline.

Recourse and non-recourse mortgage loans: If the borrower of a loan defaults on payments, then the lender can seize the property and sell it. The proceeds from the sale may be less than the outstanding mortgage balance, and not enough to recoup the losses. There are two types of mortgage loans in such cases:

__Recourse loans__: The lender can claim the shortfall (outstanding mortgage balance – after the property is sold) from the borrower. For instance, if the borrower has other properties or possessions such as an expensive car, or valuable art, then these could be sold to fulfill the shortfall.__Non-recourse loans__: Most mortgage loans are non-recourse. The lender may sell the property in case of a default and keep the proceeds. But, unlike a recourse loan, the bank/lender cannot claim other assets of the borrower to fulfill the shortfall in the outstanding mortgage balance.