Let's say an investor buys a two-year zero-coupon bond. The proceeds will equal:
X (1 + z6)6.

The investor could also buy a six-month Treasury bill and reinvest the proceeds every six months for two years. In this case, the value would be:

X (1 + z1)(1+ future rate at time 1)(1 + future rate at time 2)(1+ future rate at time 3) (1 + future rate at time 4)

Because these two investments must be equal this tells us that:

X (1 + z6)6 = X (1 + z1)(1+ future rate at time 1)(1 + future rate at time 2)(1+ future rate at time 3)

So Z6 = [(1 + z1)(1+ future rate at time 1)(1 + future rate at time 2)(1+ future rate at time 3)]¼ - 1

This equation states that the two-year spot rate depends on the current six-month rate and the following three six-month spot rates.

As we can see, short-term forward rates must equal spot rates or else an arbitrage opportunity can exist in the market place.

Compute Spot Rates if Given Forward Rates, and Forward Rates if Given Spot Rates
Computing a forward rate by using spot rates is covered above. Using spot rates, an investor can develop any forward rate.

There are two elements to the forward rate. The first is when the future rate begins. The second is the length of time for that rate. The notation is length of time of the forward rate f when the forward rate began. For example, a 2 f 8 would be the 1-year (two six-month periods) forward rate beginning four years (eight six-month periods) from now.

To solve for tFm use the following equation:

Formula 15.13

tFm =[ (1 + Zm+t)m+t / (1 + Zm)m] 1/t - 1

So for a 3f5 it would equal an equation of: [(1 + z8)8/ (1 + z5)5]1/3 -1

Example:
Z3(the 1.5 year spot rate) = 3.5%/2 = .0175
Z5 (the 2.5 year spot rate) = 4.25%/2 = .02125

Answer:
So 3f5 =[(1.02125)/ (1.0175)5]1/3 -1

S3f5 = .027916

Doubling this rate gives you a rate of 5.58%

Measuring Interest Rate Risk

Related Articles
  1. Investing

    Explaining the Spot Rate

    The spot rate is the immediate purchase price posted on exchanges for purchasing commodities, currency and securities.
  2. Investing

    What is a Forward Rate?

    Forward rate is used in both bond and currency trading to represent the current expectations of future bond interest rates or currency exchange rates.
  3. Trading

    Using Interest Rate Parity To Trade Forex

    Learn the basics of forward exchange rates and hedging strategies to understand interest rate parity.
  4. Trading

    Understanding the Spot Market

    A spot market is a market where a commodity or security is bought or sold and then delivered immediately.
  5. Trading

    Combining Forex Spot And Futures Transactions

    The spot, futures and option currency markets can be traded together for maximum downside protection and profit.
  6. Trading

    What Does Spot Price Mean?

    Spot price is the current price at which a security may be bought or sold.
  7. Trading

    The Money Market Hedge: How It Works

    Investopedia explains how to hedge foreign exchange risk using the money market, the financial market in which highly liquid and short-term instruments like Treasury bills, bankers’ acceptances ...
  8. Trading

    Why Forward Contracts Are The Foundation Of All Derivatives

    This article expands on the complex structure of derivatives by explaining how an investor can assess interest rate parity and implement covered interest arbitrage by using a currency forward ...
  9. Trading

    Forex: Gauging Forex Market Sentiment With Open Interest

    Examining open interest on currency futures can help you confirm the strength of a trend in forex market sentiment.
  10. Trading

    Using Options Tools To Trade Foreign-Exchange Spot

    Find out how delta, gamma, risk reversals and volatility can all help predict movements in the cash market.
Frequently Asked Questions
  1. What's the Best Way to Contact Warren Buffett?

    Learn how to contact Warren Buffett and what kinds of contact is most likely to receive a response from him or from his company, ...
  2. What is the Financial Services Sector?

    A diverse group of companies, beyond banks and credit unions, comprises the financial services sector.
  3. Who are Whole Foods' (WFM) main competitors?

    Whole Foods' main competitors are Sprouts Farmers Markets and Trader Joe's. However, the recent acquisition by Amazon my ...
  4. What caused the Stock Market Crash of 1929 that preceded the Great Depression?

    Find out what led to the stock market crash of 1929, which in turn led to the Great Depression. It sparked a nearly 90% loss ...
Trading Center