IFM - chapter 3 - What do interest rates mean and what is their role in valuation?

what is present value PV?

The value today of future cash flows, discounted for the time value of money. It reflects that a dollar today is worth more than a dollar in the future.

Why is Present Value important in finance?

It allows comparison of different cash flows by considering amount and timing, helping evaluate debt instruments.

What is discounting in finance?

Calculating the present value of future cash flows by adjusting for interest

What is compounding?

Calculating the future value of a cash flow by applying interest over time.

What are the 4 types of credit market instruments?

• Simple Loan

• Fixed-Payment Loan

• Coupon Bond

• Discount (Zero-Coupon) Bond

What is a Simple Loan?

A loan repaid in a single payment including principal and interest at maturity.

Define key terms for a Simple Loan.

• Loan Principal: Amount borrowed

• Maturity Date: Repayment date

• Loan Term: Time between issue and maturity

• Interest Payment: Amount paid to lender

• Simple Interest Rate: Interest/Principal (annualized)

What is Yield to Maturity (YTM)?

The interest rate that equates today's value with the present value of all future payments.

What is a Fixed-Payment Loan?

A loan repaid in equal installments (principal + interest), often monthly.

What is the Present Value of a Fixed-Payment Loan?

The sum of the present values of all payments over the loan term.

What is an annuity in finance?

• A constant cash flow

• At regular intervals

• For a finite number of periods

What is a Growing Annuity?

An annuity where the cash flow increases at a constant rate gg.

What happens when a coupon bond is priced at face value?

The yield to maturity equals the coupon rate.

How are coupon bond prices and yield to maturity related?

They are negatively related:

• If YTM increases, bond price falls.

• If YTM falls, bond price rises.

When is the yield to maturity greater than the coupon rate?

When the bond price is below its face value.

What is a consol or perpetual bond?

A bond with:

• No maturity date

• No principal repayment

• Fixed coupon payments forever

Can interest rates be negative?

Yes, but it implies paying more today than what you’ll receive in the future—this seems counterintuitive.

Why were interest rates negative in Japan, the US, and Europe?

• Japan: Bubble burst, aging population, cheap Chinese imports

• US: Treasury bills more convenient than cash

• Europe: ECB lowered rates in 2014 to spur growth post-debt crisis

What is the ex ante vs ex post real interest rate?

• Ex ante: Adjusted for expected inflation

• Ex post: Calculated after observing actual inflation

Why is the real interest rate important?

It reflects the true cost of borrowing, better shows incentives to borrow/lend, and guides credit market behavior.

When does return equal yield for bonds?

When bond maturity equals holding period.

What happens if maturity > holding period and interest rates rise?

Bond price falls → capital loss.

What is interest-rate risk?

Risk in bond returns due to interest rate changes. More maturity = more price/return volatility.

When is there no interest-rate risk?

When holding period equals maturity. Price is fixed, and return equals known YTM.

What is reinvestment risk?

When the holding period > bond maturity, reinvesting proceeds faces uncertain rates.

• Benefit if rates rise

• Loss if rates fall

what are the steps in calculating the duration of zero-coupon bonds?

1. Calculate the PV of each bond using a 10% interest rate.

2. Divide each PV by the total PV to get weights.

3. Multiply each weight by its maturity and sum them.
   → Duration = weighted average of maturities.

What does duration represent in the context of bonds?

The weighted average of the maturities of cash flows, where the weight is the proportion of the total present value.

What does Macaulay duration measure?

The effective maturity of a bond, treating coupon payments as zero-coupon bonds over time.

How is duration related to term to maturity?

Longer term to maturity ⇒ Greater duration (all else equal).

How does interest rate affect bond duration?

Interest rates ↑ ⇒ Duration of a coupon bond ↓

What effect does a higher coupon rate have on duration?

Higher coupon ⇒ Shorter duration.

Is duration additive?

Yes. The duration of a portfolio is the weighted average of the durations of its components.

How is duration used to measure interest rate risk?

it approximates the percentage price change of a bond for a small change in interest rates.

What is the relationship between duration and interest rate risk?

Greater duration ⇒ Greater percentage price change ⇒ Higher interest rate risk.