A zero-coupon yield (also called a spot rate) is the discount rate (typically default-free) at which one can equate a present value from a future cash flow for any maturity. First, it is necessary to establish some terminology. This model should prove almost instantaneous on a normal speed desktop computer and thus has a reasonable balance between speed and sophistication. The process described in this paper is a practical implementation of an old well accepted method for fitting a spline to the yield curve, which can be implemented in a spreadsheet and provide real-time estimates of the spot curve. For portfolio managers, active or indexed, often the question arises: “which bond do I buy?” A spot curve is the first step towards a process for differentiating between several similar securities, with the goal of finding relative value. Measurement of market expectations can also be the motivation, particularly for a central bank, and so a zero- coupon yield curve allows for the calculation the market expected path of short rates. Utilizing a spot curve for agency securities, it is possible to calculate a theoretical price for the security that is consistent with currently traded securities. For example, suppose an investment dealer is offering for sale a particular US agency security, newly issued. Security valuation is the most common, where interpolation of spot rates for specific dates is necessary.
1Įlectronic copy available at: The motivations for creating a spot curve can be numerous. This paper presents an alternative approach which provides a good trade-off between sophistication and ease of implementation *This suggested approach should only be used for asset valuation in a portfolio management context, and not for market-making applications. Dozens of methods and models exist for calculating the spot curve, most requiring either well-prepared data, copious amounts of computer programming, or significant computing power. Introduction The zero-coupon yield curve (or spot curve) could be considered the single most important tool for the fixed-income portfolio manager and investment analyst.
The approach uses a McCullough cubic spline and can be estimated using restricted least squares in Excel which provides a considerable advantage over other more advanced, but not necessarily more accurate models.
Electronic copy available at: A real-time zero-coupon yield curve cubic spline in Excel * Robert Scott Schroders Investment Management 31 Gresham Street, London UK, EC2V 7QA Abstract This paper details a method for estimating a zero-coupon yield curve using a set of securities data.
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