Creating a Risk-Free Portfolio in Excel

A risk-free portfolio is a portfolio that has no risk of losing money, regardless of how the market performs. This means that the portfolio’s return is certain and predictable, and does not depend on any random factors. A risk-free portfolio is usually composed of a risk-free asset and a risky asset, where the risk-free asset is an investment that has a guaranteed return and no possibility of default, such as a U.S. Treasury bill, and the risky asset is an investment that has a higher return but also a higher chance of losing value, such as a stock or a bond.

The idea behind a risk-free portfolio is to combine the risk-free asset and the risky asset in such a way that the portfolio’s risk is zero, or in other words, its beta is zero. Beta is a measure of how sensitive an asset or a portfolio is to the movements of the market. A beta of zero means that the portfolio is not affected by the market at all, and its return is independent of the market return. A beta of one means that the portfolio moves exactly in sync with the market, and its return is equal to the market return. A beta of less than one means that the portfolio is less volatile than the market, and its return is lower than the market return. A beta of more than one means that the portfolio is more volatile than the market, and its return is higher than the market return.

For example, suppose an investor wants to create a risk-free portfolio with a risk-free asset that has a return of 2% and a beta of zero, and a risky asset that has a return of 10% and a beta of 1.5. Using the formula above, the investor would have to invest 0% of the portfolio in the risk-free asset and 100% of the portfolio in the risky asset, which would result in a portfolio return of 10% and a portfolio beta of zero. This means that the portfolio would have the same return as the risky asset, but without any risk.

However, in reality, a risk-free portfolio is very difficult to achieve, because there is no such thing as a truly risk-free asset. Even U.S. Treasury bills have some degree of risk, such as inflation risk, interest rate risk, and reinvestment risk. Moreover, the beta of an asset or a portfolio can change over time, depending on the market conditions and the investor’s expectations. Therefore, a risk-free portfolio is more of a theoretical concept than a practical one, and it is used to illustrate the trade-off between risk and return in portfolio management.

Basic Theory:

A risk-free portfolio consists of assets with a guaranteed return, typically considered to be free of market risk. Traditionally, government securities, such as Treasury bills or bonds, are considered risk-free due to their low default risk.

The formula for calculating the return of a risk-free portfolio is straightforward:

$R_f = \frac{F - P}{P}$

Where:

$R_f$ is the risk-free rate of return.
$F$ is the future value of the investment.
$P$ is the initial investment (present value).

Procedures:

Identify Risk-Free Assets: Choose assets with minimal risk, such as government bonds or Treasury bills.
Calculate Risk-Free Rate: Use historical data or financial news to determine the current risk-free rate.
Construct Portfolio: Allocate funds to the selected risk-free assets.
Calculate Portfolio Return: Utilize the formula $R_f = \frac{F - P}{P}$ to calculate the expected return of the portfolio.

Example Scenario:

Let’s consider a scenario where an investor allocates $50,000 to a Treasury bond with a face value of $52,000, set to mature in one year. The current market price of the bond is $50,500.

$R_f = \frac{52,000 - 50,500}{50,500}$

$R_f \approx 0.0298$

In this scenario, the risk-free rate of return is approximately 2.98%.

Excel Calculation:

Investment	Initial Investment (P)	Future Value (F)	Risk-Free Rate (Rf)
Treasury Bond	$50,500	$52,000	= (F – P) / P
Result	=$50,500	=$52,000	=($C$3 – $B$3) / $B$3

Result: Risk-Free Rate ( $R_f$ ) = 2.98%

Other Approaches:

Zero-Coupon Bonds: Invest in zero-coupon bonds that don’t pay interest but are issued at a discount, providing a fixed return at maturity.
Money Market Instruments: Consider short-term money market instruments, like certificates of deposit (CDs) or commercial paper, as they are relatively low-risk.
Derivatives: Explore the use of financial derivatives, such as interest rate swaps, to hedge against interest rate risk.