Keep in mind the FRM views a mortgage (or MBS) as firstly akin to a bond with an embedded option. The homeowner is like an issuer of a callable bond, where the call tends to be exercised when the market value of the outstanding loan exceeds the loan balance due to lower rates. This prepayment option induces the negative convexity in the P/Y relationship. IMO, grasp this first -- David
AIM: Describe the mortgage prepayment option and the factors that influence prepayments.
Questions:
103.1. On January 1st, the Smiths bought a house with a 30-year, 6.0% fixed-rate $120,000 mortgage loan; i.e., the 6.0% stated annual rate is payable (compounds) monthly. The monthly payment is $791.46. After eleven months and eleven monthly payments, on November 1st, the loan balance is $118,652.58. After one further monthly payment, at the end of December, what will be the new loan balance?
a. $117,933.12
b. $118,133.12
c. $118,526.38
d. $118,611.25
103.2. In regard to a mortgage loan and prepayment, each of the following is true EXCEPT:
a. At all times during the life of the mortgage loan, the mortgage rate is the internal rate of return (IRR) on the loan held to maturity
b. At all times during the life of the mortgage loan, the mortgage rate is the yield to maturity (YTM) on the loan held to maturity
c. When interest rates decline, the market value of the mortgage owner's liability, P(t), increases; if this value, P(t) increases above the principal remaining, L, it becomes advantageous for the homeowner to refinance the mortgage
d. Prepayment is costly to the bank because the bank forgoes the higher mortgage rate in favor of a lower market rate; therefore, the bank obtains partial compensation in the (higher) mortgage rate
103.3. According to Veronesi, each of the following is true about mortgage prepayments EXCEPT:
a. Summers are characterized by large prepayments; this is called "seasonality"
b. The prepayment rate tends to be slow (low) in the early years of a mortgage
c. As property values decline, prepayments tend to decline
d. Mortgage pools that refinanced heavily in the past tend to refinance again at higher-than-average rates; this is called "loyalty of repeat customers"
Answers:
AIM: Describe the mortgage prepayment option and the factors that influence prepayments.
Questions:
103.1. On January 1st, the Smiths bought a house with a 30-year, 6.0% fixed-rate $120,000 mortgage loan; i.e., the 6.0% stated annual rate is payable (compounds) monthly. The monthly payment is $791.46. After eleven months and eleven monthly payments, on November 1st, the loan balance is $118,652.58. After one further monthly payment, at the end of December, what will be the new loan balance?
a. $117,933.12
b. $118,133.12
c. $118,526.38
d. $118,611.25
103.2. In regard to a mortgage loan and prepayment, each of the following is true EXCEPT:
a. At all times during the life of the mortgage loan, the mortgage rate is the internal rate of return (IRR) on the loan held to maturity
b. At all times during the life of the mortgage loan, the mortgage rate is the yield to maturity (YTM) on the loan held to maturity
c. When interest rates decline, the market value of the mortgage owner's liability, P(t), increases; if this value, P(t) increases above the principal remaining, L, it becomes advantageous for the homeowner to refinance the mortgage
d. Prepayment is costly to the bank because the bank forgoes the higher mortgage rate in favor of a lower market rate; therefore, the bank obtains partial compensation in the (higher) mortgage rate
103.3. According to Veronesi, each of the following is true about mortgage prepayments EXCEPT:
a. Summers are characterized by large prepayments; this is called "seasonality"
b. The prepayment rate tends to be slow (low) in the early years of a mortgage
c. As property values decline, prepayments tend to decline
d. Mortgage pools that refinanced heavily in the past tend to refinance again at higher-than-average rates; this is called "loyalty of repeat customers"
Answers:
