Interest Archives - Page 7 of 7 - treasuryXL

Yield Curves (term structure of interest rates) – filling in the blanks part II

| 03-06-2016 | Lionel Pavey |

Most treasurers do not have access to a dedicated financial data vendor (Bloomberg, Reuters) but are regularly faced with having to discover prices related to yield curves. There are websites that can provide us with relevant data, but these are normally a snapshot and not comprehensive – the data series is incomplete. It is therefore up to the treasurer to complete the series by filling in the blanks. In my previous article I went over the first approach. Today I’ll talk about the second approach.

A second approach would be to apply a weighting to the known periods of the par curve and to average the difference out over the missing periods.

This leads to 1 year constant maturity rates that are almost equal in value for all the periods between 2 known periods. Whilst these forward rates are also not correct they at least supply us with a visual indicator as to the general shape of the forward yield curve – the 1 year constant maturity rates

reach their zenith between years 12 and 14; after that point they then start to decrease.

Futhermore, taking into consideration the yield curve as shown in the graph, we can make the following conclusions about the 1 year curve:-

11 year rate must be higher than the linear interpolated rate but lower than the weighted interpolated rate
13 year rate must be higher than the weighted interpolated rate
15 year rate must be lower than the linear interpolated rate and lower than the weighted interpolated rate
16 year rate must be higher than the linear interpolated rate and higher than the weighted interpolated rate
20 year rate must be lower than the linear interpolated rate and lower than the weighted interpolated rate
The implied forward 1 year constant maturity curve must be smooth and monotonic.

On the basis of these restraints a par curve can be built that leads to the following forward curve.

The rates for the missing periods have been calculated manually whilst adhering to the conditions mentioned before– there are formulae which would allow rates to be discovered (Cubic spline, Nelson Siegel etc.) – but these rely on random variables and I have yet to see anyone quote and trade prices based solely on a mathematical formulae.

Visually, the 1 year curve meets all the criteria for the construction of a yield curve, together with the underlying par and zero yield curves.

To ascertain that the rates are correct, discount all the cash flows of the par yield for the given maturity – they should equal 100.

Here is an overview of all the implied 1 year rates using the different methods to construct the yield curve.

Conclusion:

For a quick calculation a straight line interpolation is acceptable with the warning that with a normal positive yield curve the real prices will be higher than the prices calculated by straight line interpolation. For a negative yield curve this would be reversed – real prices lower than interpolated prices.

The average difference between the par yield prices of the adjusted smooth yield and the straight interpolation yield are only 2.5 basis points. However, this difference is magnified when looking at a 1 year forward yield curve where the average difference is 22.5 basis points per period with a maximum of 53.5 basis points.

Next – Zero Coupon Yields and implied Forward Yields

Would you like to read part one of this article?
– Yield Curves (term structure of interest rates) – filling in the blanks

Lionel Pavey

Treasurer

Yield Curves (term structure of interest rates) – filling in the blanks

| 27-05-2016 | Lionel Pavey

Most treasurers do not have access to a dedicated financial data vendor (Bloomberg, Reuters) but are regularly faced with having to discover prices related to yield curves. There are websites that can provide us with relevant data, but these are normally a snapshot and not comprehensive – the data series is incomplete. It is therefore up to the treasurer to complete the series by filling in the blanks.

A quick refresher about the construction of a yield curve raises the following points:-

All data must be from the same market (treasury bonds, Interest Rate Swaps (IRS) etc.)
A regular term (maturity) is preferred for ease of construction
A curve must be smooth
An implied zero yield curve can be built from the smooth par curve – a theoretical yield curve where no interest is paid until maturity. In a bond this would redeem at par (100) and be issued at a deep discount to par
A series of discounted cash flow factors (DCF) are produced
An implied forward curve with constant maturities can be built from the par curve
An implied forward curve must be monotonic – each point in an increasing sequence is greater than or equal to the preceding point, each point in a decreasing sequence is smaller than or equal to the preceding point

If we look at IRS par yield prices that can be found on a website, we can regularly see yield prices for periods from 1 year to 10 year inclusive, a 15 year price and a 20 year price. To construct a complete curve from 1 year up to and including 20 years we need to fill in the blanks at 11,12,13,14,16,17,18 and 19 years. These yields are assumed to be par yields – the coupon rate is equal to the yield to maturity and the instrument trades at par.

Before starting let us define the procedure for constructing a par yield curve:-
The methodology used is called “bootstrapping”. This allows us to extract discount factors (DCF) from the market rates. DCF’s allow us to calculate a value today for a cash flow in the future.

We assume that the nominal value for all calculation purposes is 100

For a 1 year rate we know the interest and redemption amount at maturity. A DCF is built whereby the net present value (NPV) of these future cash flows in 1 years’ time is equal to 100 or par.

For a 2 year rate we receive interest after 1 year and interest and redemption amount at maturity.

We discount the 1^st years’ interest with the DCF we obtained from the 1 year rate and deduct this amount from our initial nominal of 100. This net amount is then divided by the interest and redemption at maturity (at end of 2 years) to obtain the DCF for the 2 year rate.

Example:

1 Year 7% 2 Year 9%

1 Year
100 / (7/100+100) = 0.93457944 (DCF)

2 Year
9 * 0.93457944 = 8.41121496
100 – 8.41121496 = 91.58878504
91.58878504 / (9/100+100) = 0.8402640829

These DCF’s can then be used to find the NPV of any cash flow maturing in 1 or 2 years’ time.

The following example shows a yield curve from February 2013 published on the website of an interbank broker.

yield curve February 2013

The quickest way to price the missing periods would be with straight line interpolation of the par curve between the known points – which would produce the following par curve, zero yield curve and forward curve with constant 1 year maturity.

yield curve February 2013

Straight line interpolation

Whilst the par curve and zero curve are smooth, the implied 1 year constant maturity curve is jagged and certainly neither smooth nor monotonic. The 11^th 1 year period rate is lower than the 10^th period and the 15^th 1 year period rate is higher than the 16^th period.

A second approach would be to apply a weighting to the known periods of the par curve and to average the difference out over the missing periods. Read more on this second approach in my next article which will appear next week.

Lionel Pavey

Treasurer

Short note on interest rate derivatives

16-05-2016 | by Ad van der Plas |

They are often in the news, but what are they and how do they work? Interest rate derivatives are derivatives of the money- and capital markets and are especially designed to give assurance on the interest rate you will have to pay or receive in the future. Best known is the interest rate swap, a swap between the fixed and variable interest rate. All other interest derivatives are calculated on the interest rate swap. How does this swap work?

The interest rate swap is a two party agreement, usually in ISDA model, in which the fixed and variable interest amounts are swapped. The swap period, the fixed and variable (reference) interest rate are defined. The interest is calculated on the agreed notional principal amount and the interest amounts are payable on the payment dates. One party receives the fixed rate amounts and pays the variable rate, and the other party receives the variable rate amounts and pays the fixed rate.

With buying an interest rate swap, you can change the interest rate risk of an underlying loan from an uncertain variable rate to a certain fixed rate. That is….if during the swap period there are no changes in the loan itself. Since you aim to obtain certainty you should be aware of potential uncertainties during the swap period, such as:

A change of the reference rate in terms of content or effective representation (Libor).
A change in the interest rate calculation of the loan caused by regulatory changes in the financial markets (Solvency) or due to balance sheet effects of the lending company itself like a liquidity surcharge.
The lender changes the surcharge because he has revised the credit rate of your company.
The underlying loan is canceled or restructured.
The counterparty in the swap agreement requires an additional payment if the swap has a negative value.
Possible P&L and Balance sheet effects due to changes in the valuation of the swap because of changes in regulations, for example IFRS.
A different interpretation of the regulations when changing your auditor.

Please also note that the outstanding swap agreements will have effect on your total financing capacity. And finally, a warning: improper use of derivatives can be a big risk. Be sure to have a professional opinion when using derivates.

Ad van der Plas

Independent Treasury Consultant & Interim Manager

Negative Interest Rate Policy: No lasting effect on FX

14-04-2016 | by Simon Knappstein |

Negative interest rates are gripping Central Banks worldwide. The BoJ has resorted to this unexpected and unusual policy at the end of January. The ECB is expected to dig deeper into negative realms at their March meeting. The Swedish Riksbank has also gone negative and the Fed is contemplating the possibility for the eventuality economic growth will falter and inflation will fall. And of course the Swiss are already quite accustomed to negative interest rates. But in the FX markets the effects are minimal and short-lived.

So, are Central banks reaching the end of the effectiveness of their extremely loose monetary policies? If so, the big question is what next? Plain currency intervention? Hard to imagine currently, though the Swiss National Bank is said to be continuously intervening to prop up EUR/CHF.

The ECB has crossed the zero interest rate border in the summer of 2014 bringing its depo-rate to minus 0.10%. A move intended to stimulate credit growth by commercial banks, and as a means to lower the value of the Euro as to import more inflation. Although the latter was not explicitly mentioned everyone knows it was.

Since then the Swiss National Bank in December 2014, the Riksbank in February 2015 and the Bank of Japan in January 2016 have followed suit by introducing negative interest rates.

Currency impact

Figure 1 – Currency impact

The impact on the currency exchange rate is questionable and certainly not a straightforward main driver, as can be seen in figure 1.
When the ECB introduced a negative interest rate in the summer of 2014 it was accompanied by the start of the QE program and indeed EUR/USD moved considerably lower. The rate cut to -0.3% last December had no material impact on the exchange rate, even though it was followed by the first Fed rate hike in years.

The pressure on EUR/CHF could not be relieved by a rate cut to -0.25% in December 2014 so it was soon followed by the abandoning of the minimum exchange rate at 1.20 and a further cut to -0.75%. EUR/CHF stabilized but only continuous intervention by the SNB has brought the pair higher since then. The charts for EUR/SEK and USD/JPY speak for itself.

The conclusion is that there is very little to no evidence that negative interest rates lead to weaker currencies to support inflationary pressures.

Simon Knappstein

Owner of FX Prospect

Yield Curves (term structure of interest rates) – filling in the blanks part II

Conclusion:

Yield Curves (term structure of interest rates) – filling in the blanks

Example:

Short note on interest rate derivatives

Negative Interest Rate Policy: No lasting effect on FX

Currency impact

Go to

Partner Program

Contact us

Subscribe