Basis risk

In theory the futures market provides a fixed and stable outcome when hedging currency or interest rate risk, but in practice futures contracts are exposed to basis risk.

Basis is the difference between the futures and spot prices and, for the purposes of recommending a hedging strategy, it is often assumed to diminish at a constant rate. Basis risk arises when the price of a futures contract does not have a predictable relationship with the spot price of the instrument being hedged. When basis risk is introduced to a scenario, it may mean an alternative hedging method would provide a better result.

In order to illustrate this point, we will use the information provided in a sample question from the September/December 2017 exam sessions, Wardegul Co, and investigate the impact of basis risk on the hedging recommendation. The company’s treasury department would like to hedge the following transaction.

Transaction to be hedged

Today’s date is 1 October 2017. The treasury department plans to hedge a receipt, in Eurian Dinar (D), of D27m. The receipt is expected on 31 January 2018 and will need to be invested until 30 June 2018.

The central bank base rate in Euria is currently 4·2% and the treasury team believes that it can invest funds in Euria at the central bank base rate less 30 basis points. However, treasury staff have seen predictions that the central bank base rate could increase by up to 1·1% or fall by up to 0·6% between now and 31 January 2018.

For the purposes of this example we will consider the following possibilities to hedge the receipt:

  • Interest rate futures
  • Exchange-traded options on interest rate futures

Three month D futures, D500,000 contract size

Prices are quoted in basis points at 100 – annual % yield:

December 2017:

94.84

March 2018:

94.78

June 2018:

94.66

Exchange-traded options on three month D futures, D500,000 contract size, option premiums are in annual %

 

Calls

 

Strike price

 

Puts

 

December

March

June

 

December

March

June

0.417

0.545

0.678

 

0.071

0.094

0.155

0.078

0.098

0.160

 

0.393

0.529

0.664

Assume futures and options contracts are settled at the end of each month.

In the first instance we will follow the approach used in the past exam question and assume there is no basis risk and that basis diminishes at a constant rate, based on monthly time intervals. We will then introduce basis risk and consider the impact on our recommended hedging strategy.

(1) Ignore basis risk (as per sample question)

Futures
Wardegul Co’s treasury department would buy March futures as the hedge is against a fall in interest rates and the investment will be made on 31 January.

Number of contracts = D27,000,000 / D500,000 × 5 months / 3 months = 90 contracts

Unexpired basis
Spot price (1 October) – futures price = basis
(100 – 4.20) – 94.78 = 1.02
Unexpired basis on 31 January = 2/6 × 1.02 = 0.34

If central bank base rate increases to 5.3%

 

D

Investment return 5.0% x 5/12 x D27,000,000

562,500

Expected futures price: 100 – 5.3 – 0.34 = 94.36

 

Loss on the futures market: (0.9436 – 0.9478) × D500,000 × 3/12 × 90

(47,250)

Net receipt

515,250

Effective annual interest rate 515,250 / 27,000,000 x 12/5

4.58%

If central bank base rate falls to 3.6%

 

D

Investment return 3.3% x 5/12 x D27,000,000

371,250

Expected futures price: 100 – 3.6 – 0.34 = 96.06

 

Profit on the futures market: (0.9606 – 0.9478) × $500,000 × 3/12 × 90

144,000

Net receipt

515,250

Effective annual interest rate 515,250 / 27,000,000 x 12/5

4.58%

Options on interest rate futures

The treasury department would buy March call options to hedge against a fall in interest rates. As above, 90 contracts are required.

If central bank base rate increases to 5.3%

Exercise price

94.25

95.25

Expected futures price, as above

94.36

94.36

Exercise?

Yes

No

Gain in basis points

11

0

 

D

D

Investment return as above

562,500

562,500

Profit on option

 

0

0.0011 × $500,000 × 3/12 × 90

12,375

 

Premium

 

 

0.00545 x D500,000 x 3/12 x 90

(61,313)

 

0.00098 x D500,000 x 3/12 x 90

 

(11,025)

Net receipt

513,562

551,475

Effective annual interest rate

 

 

513,562 / 27,000,000 × 12/5

4.56%

 

551,475 / 27,000,000 × 12/5

 

4.90%

If central bank base rate falls to 3.6%

Exercise price

94.25

95.25

Expected futures price, as above

96.06

96.06

Exercise?

Yes

Yes

Gain in basis points

181

81

 

D

D

Investment return as above

371,250

371,250

Profit on option

 

0

0.0181 × $500,000 × 3/12 × 90

203,625

 

0.0081 × $500,000 × 3/12 × 90

 

91,125

Premium as above

(61,313)

(11,025)

Net receipt

513,562

451,350

Effective annual interest rate

 

 

513,562 / 27,000,000 × 12/5

4.56%

 

451,350 / 27,000,000 × 12/5

 

4.01%

Comments
As expected, the futures market provides a fixed return of 4.58% whether the central bank base rate increases to 5.3% or reduces to 3.6%. The 95.25 option provides a better outcome as long as interest rates rise but is significantly lower if interest rates fall. If the board is at all risk averse the futures outcome would be preferable. The 94.25 option is marginally lower than the futures outcome under both scenarios but may be preferable if the base rate rises higher than 5.41%, the point at which the option would not be exercised.

(2) Impact of basis risk

Today’s date is 31 January. The prediction that the central bank base rate might increase by 1.1% to 5.3% turns out to be exactly correct. Based on our previous basis calculation we would have expected today’s price for the March futures contracts to fall to 94.36.

However, futures contracts are exposed to basis risk, which means the closing March futures price on 31 January could be more or less than predicted. For the purposes of this example, we will assume the closing futures price on 31 January is 94.16, only marginally less than our prediction from before.

Futures

Central bank rate increases to 5.3%

 

D

Investment return as above

562,500

Loss on the futures market: (0.9416 – 0.9478) × $500,000 × 3/12 × 90

(69,750)

Net receipt

492,750

Effective annual interest rate 492,750 / 27,000,000 x 12/5

4.38%

Options on interest rate futures

If central bank base rate increases to 5.3%

Exercise price

94.25

95.25

Futures price, as above

94.16

94.16

Exercise?

No

No

 

D

D

Investment return as above

562,500

562,500

Premium

(61,313)

(11,025)

Net receipt

501,187

551,475

Effective annual interest rate

 

 

501,187 / 27,000,000 × 12/5

4.45%

 

551,475 / 27,000,000 × 12/5

 

4.90%

Implications for hedging strategy

The futures market provides a lower return than both option contracts although we have already determined that a risk averse treasury manager would have ignored the 95.25 option. However, the 94.25 option now looks more attractive than the futures outcome even though the central bank base rate increased exactly as predicted.

If the relationship between the futures and spot price is not predictable, there is no guarantee that the closing futures price on 31 January will match the price predicted by our basis calculation. On 1 October the futures price prediction for 31 January is 94.36, assuming the base rate increases to 5.3%, but it could be either more or less even when the base rate increases exactly as predicted.

This exposure to basis risk means the actual futures price fell to 94.16 on 31 January instead of 94.36. An unexpected change in basis, even marginally, reduces the return on the futures hedge from 4.58% to 4.38% as opposed to a return of 4.45% using the 94.25 option. With the benefit of hindsight the 94.25 option would have provided a better outcome. However, the treasury department have limited visibility of the future when choosing an optimal strategy at the time the hedge is set up on 1 October. The treasury department’s best estimate of the closing futures price is based on a simplifying assumption that basis diminishes at a constant rate, which may not hold true in practice. Basis risk, therefore, introduces an element of unpredictability which the treasury staff need to be aware of at the outset. Scenario analysis would be useful in determining the final strategy in accordance with the company’s risk preferences.

Written by a member of the AFM examining team