Understanding Spot Rates in Excel

A spot rate is the current market price of an asset that is available for immediate delivery. It is based on the supply and demand of the asset, as well as the expectations of future market conditions. Spot rates can be quoted for different types of assets, such as currencies, commodities, securities, or interest rates.

For example, the spot rate of a currency pair is the exchange rate between two currencies at a given moment. It reflects how much one currency is worth in terms of another currency. The spot rate of a currency pair can change frequently due to various factors, such as economic data, political events, or market sentiment. The spot rate of a currency pair is usually expressed as the number of units of one currency that can be exchanged for one unit of another currency. For example, the spot rate of USD/JPY is 113.25, which means that one US dollar can be exchanged for 113.25 Japanese yen.

The spot rate of a commodity is the price of a specific quantity and quality of a commodity at a specific location and time. It reflects the current supply and demand of the commodity, as well as the expectations of future market conditions. The spot rate of a commodity can vary depending on the location, transportation, storage, and delivery costs of the commodity. The spot rate of a commodity is usually expressed as the amount of money that can be paid for one unit of the commodity. For example, the spot rate of crude oil is $68.32 per barrel, which means that one barrel of crude oil can be bought for $68.32.

The spot rate of a security is the price of a security that is traded in the secondary market. It reflects the current value of the security, as well as the expectations of future cash flows and risks. The spot rate of a security can change due to various factors, such as the performance of the issuer, the market interest rates, the credit ratings, or the market liquidity. The spot rate of a security is usually expressed as the amount of money that can be paid for one unit of the security. For example, the spot rate of a bond is $102.50, which means that one bond with a face value of $100 can be bought for $102.50.

The spot rate of an interest rate is the interest rate that is applied to a single payment that is made at a specific time in the future. It reflects the current market value of money, as well as the expectations of future inflation and risk. The spot rate of an interest rate can be derived from the prices of zero-coupon bonds, which are bonds that pay no interest until maturity. The spot rate of an interest rate is usually expressed as an annual percentage rate. For example, the spot rate of a one-year interest rate is 2.5%, which means that the interest rate that is applied to a single payment that is made one year from now is 2.5%.

Basic Theory of Spot Rates:

A spot rate, also known as a zero-coupon rate, is the interest rate at which an investor can lend or borrow money for a specified period. The spot rate is derived from the yield curve, which represents the relationship between interest rates and the time to maturity of securities. In essence, it reflects the market’s expectations for future interest rates.

The spot rate for a specific maturity date is considered the risk-free rate for that period. Investors often use spot rates to discount future cash flows, especially when valuing fixed-income securities.

Procedures for Quoting Spot Rates in Excel Formulas:

To calculate spot rates in Excel, we can use the following formula:

$Spot \ Rate = \left( \frac{Face \ Value}{Present \ Value} \right)^{\frac{1}{n}} - 1$

Where:

$Face \ Value$ is the future value of the bond or security.
$Present \ Value$ is the current value of the bond or security.
$n$ is the number of periods to maturity.

Example Scenario:

Let’s consider a bond with a face value of $1,000, a current market value of $950, and 5 years to maturity.

$Spot \ Rate = \left( \frac{1000}{950} \right)^{\frac{1}{5}} - 1$

Calculating this in Excel:

Open a new Excel spreadsheet.
Enter the values in cells A1, B1, and C1 for Face Value, Present Value, and Years to Maturity, respectively.
In cell D1, enter the formula $Spot \ Rate = \left( \frac{A1}{B1} \right)^{\frac{1}{C1}} - 1$ .

The Result:

The calculated spot rate will be displayed in cell D1. In our scenario, the spot rate is approximately 0.0107 or 1.07%.

Other Approaches:

Yield Function in Excel: Excel provides a built-in function for calculating yields, including spot rates. The formula is $\text{YIELD}(\text{Settlement}, \text{Maturity}, \text{Rate}, \text{Price}, \text{Redemption}, \text{Frequency}, \text{Basis})$ .
Using Solver: For a more iterative and precise approach, you can use the Solver add-in to find the spot rate that minimizes the difference between the observed and calculated bond prices.