Australian Government Zero Coupon Yield Curves

The following compares the traded coupon par yields for Australian Government Bonds and the provides estimates of the zero coupon yields and a number of common yield curve smoothing techniques. Australian Government Treasury Bond Yield Curve is updated weekly from RBA Table F16. The data in this tool has been reduced down to the mid week (Wednesday) data (or the closest equivalent when Wednesday falls on a public holiday).

The latest data date is .

Yield curve smoothing methods

Nelson Siegel

The Nelson Siegel interest rate fitted yield curve is derived from the following non-linear equation:

Or often .

Svensson

The Svensson model is an extension which includes an extra term to allow for extra curvature. This curvature can result in over-fitting and a lack of stability at the extremes of the observed terms. This is occasionally evident on very short term rates, for instance terms of less than 1 month.

Merryl Lynch Exponential Spline (MLES)

Discount function is given by:

where is the exponential smoothing spline, there are N splines, the choice of which balances smoothness and fit to the variation in the data.

Spot yield curve

Note that prior to 2014 the number of traded bonds was very small and hence fitted yield curve extrapolated to the extremes produce illogical predictions. These are included in the selection below for illustrative purposes.

Yield curve for

Forward yield curve

Instanteous forward rate is the market implied expectation for the annual (1 year interest) at each term in the futre. It is derived from the derivative of the spot rate with respect to term:

For a Svensson type yield curve the forward rate is given by:

Time series of rates by term

Select a term the interpolated yields are produced for the full time series, using the selected yield curve smoothing technique. An inverted yield curve, when the short end rates are greater than long end rates, are highlighted in red.

Bond mark-to-market by holding period

Using the term structure the gain or loss holding a bond of a particular investment tenor over a holding period is calculated as the difference ratio of the zero coupon yields (z) on the investment date (0) for the investment term (T) and the zero coupon yield on the mark to market date (t) for the residual term (T-t):

In practice bonds typically pay semi-annual coupons. The mark to market here applies to zero coupon bonds in which all interest and principal is received at maturity. This calculation therefore exagerates the variation in the mark-to-market.