Chapter 61t: Bill Yield - Assume An Investor Purchased A Six

Chapter 61t Bill Yieldassume An Investor Purchased A Six Month T Bill

Assess the calculation of yield based on a six-month T-bill purchase and sale, including the relationship between purchase price, sale price, and yield. Evaluate how changes in purchase price, sale price, and holding period affect the annualized yield of T-bills, explaining the underlying logic for each scenario.

Paper For Above instruction

The calculation of the yield on a Treasury bill (T-bill) involves understanding the relationship between the purchase price, the sale price, and the holding period. A T-bill purchased at a discount and sold at a higher price prior to maturity yields a return that can be annualized depending on the investment period. When an investor purchases a T-bill at $9,000 with a face value of $10,000, and sells it 90 days later for $9,100, the yield can be computed using the formula:

Yield = [(Sale Price - Purchase Price) / Purchase Price] × (360 / Days Held)

Plugging in the numbers, the yield is:

Yield = [($9,100 - $9,000) / $9,000] × (360 / 90) = ($100 / $9,000) × 4 = 0.0111 × 4 = 0.0444 or 4.44% annualized yield.

This reflects the fact that the return over the 90-day holding period is scaled up to an annual figure. Now, considering how adjustments in purchase price, sale price, or duration affect yield, the logic is straightforward: a lower purchase price increases yield, a higher sale price increases yield, and a shorter holding period (fewer days) increases annualized yield, assuming constant absolute gains.

Specifically, if the purchase price decreases (keeping sale price and period constant), the yield increases because the discount achieved at purchase becomes larger relative to the initial investment. Conversely, if the sale price decreases (keeping purchase price and period constant), yield decreases because the return on the investment shrinks. When the number of days held decreases, the annualized yield increases—since the same profit over a shorter period is extrapolated over a year—highlighting the inverse relationship between duration and annualized rate in yield calculations.

Impact of Yield Changes and Duration on T-Bill Returns

The relationship between the purchase and sale prices and the yield is crucial for understanding T-bill investments. A lower purchase price or higher sale price yields a higher return, but these gains must be considered in context of the time frame. Short durations amplify the annualized yield compared to longer durations when the absolute gains stay fixed, reflecting the time value of money. This dynamic underscores the importance of considering both absolute profit and the period over which it occurs when evaluating treasury securities.

In sum, investors should recognize that modifications in purchase price, sale price, and holding period significantly influence the annualized yield. These relationships form the foundation of fixed-income security valuation and investment strategies, guiding investors on how to optimize returns relative to risk and duration.

References

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