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# spot-rates

1. ### YouTube T3-11: Forward rates are implied by zero rates

Forward rates link two zero (aka, spot) rates by ensuring your expected return is the same between two choices: (1) invest at the longer-term spot rate versus (2) invest at the shorter-term spot rate and "roll over" into the implied forward rate. This is an implied forward rate that ignores...
2. ### YouTube T3-10: Yield to Maturity Interpretations

Superficially, the yield to maturity (YTM, aka yield) simply inverts the usual time value of money (TVM) inputs by solving for the yield as a function of four inputs: face (future) value, coupon (payment), maturity (time), and current price (present value). But in terms of interpretation, I...
3. ### YouTube T3-09: Theoretical price of a bond using spot rates

The theoretical bond price is the present value if the future cash flows are discounted at the spot (aka, zero rates); in other words, it is the price given by discounted cash flow (DCF). We don't expect the traded (observed) price to exactly match because the DCF price is fundamental, yet...
4. ### P1.T4.906. Annuities and yield to maturity (Tuckman Ch.3)

Learning objectives: Compute a bond’s YTM given a bond structure and price. Calculate the price of an annuity and a perpetuity. Explain the relationship between spot rates and YTM. Questions: 906.1. Exactly one year ago, Sally purchased a \$100.00 face value bond that pays a semi-annual coupon...
5. ### P1.T4.903. Spot, forward and par rates (Tuckman Ch. 2)

Learning objectives: Interpret the forward rate, and compute forward rates given spot rates. Define par rate and describe the equation for the par rate of a bond. Interpret the relationship between spot, forward, and par rates. Questions: 903.1. Assume the following discount function (note...
6. ### P1.T4.902. Swap rates versus spot rates (Tuckman Ch. 2)

Learning objectives: Calculate and interpret the impact of different compounding frequencies on a bond’s value. Calculate discount factors given interest rate swap rates. Compute spot rates given discount factors. Questions: 902.1. Analyst Patricia is analyzing the following four bonds: Bond...
7. ### P1.T3.713. Spot and forward rates in bond pricing (Hull Chapter 4)

Learning objectives: Calculate the theoretical price of a bond using spot rates. Derive forward interest rates from a set of spot rates. Derive the value of the cash flows from a forward rate agreement (FRA). Questions: 713.1. Consider the steep spot (aka, zero) rate curve illustrated below...
8. ### P1.T4.316. Tuckman's yield to maturity (YTM)

AIMs: Define, interpret, and apply a bond’s yield-to-maturity (YTM) to bond pricing. Compute a bond's YTM given a bond structure and price. Explain the relationship between spot rates and YTM. Calculate the price of an annuity and a perpetuity. Questions: 316.1. Assume the following 2-year...
9. ### How to derive forward interest rates from spot rates (Hull vs Tuckman)

Hi! I'm confused about forward interest rate calculation, Hull (ch 4) uses RF=(R2T2-R1T1)/(T2-T1), Tuckman (ch 2) instead computes from formula (1+r(0,2)/2)^4=(1+r(0,1.5)/2)^3+(1+f(1.5,2.0)/2)^1. I'm sure the answer is just here but I can't see... Is it about compounding? Should I memorize both...