Cash and carry pricing

If you want to own a bond on a future date, you have two routes. Buy it now and hold it — "cash and carry" — or buy a futures contract now and take the bond later.

If both routes end with the same bond on the same date, they should cost the same. Otherwise everyone would take the cheaper route and sell the dearer one. The cash and carry model turns that argument into a price.

The workbook states the result for a single bond future, based on the concept that there is no arbitrage between the underlying and the future bond price:

Future bond price = Cash price + financing cost − income on cash position

Buying now costs you the price plus the interest on the money you tied up. But holding the bond also earns you its interest. The futures price is what is left.

The three components, as the workbook defines them:

Conventions in the workbook's example: G-Secs settle T+1, accrued interest is on a 30/360 basis, and financing cost is on an Actual/365 basis on the dirty price.

The basis. The difference between spot and futures price is the basis. The workbook observes that in bond futures basis is positive most of the time, because income on the cash position is more than the financing cost — so bond futures generally trade at a discount.

The assumptions. The model assumes the underlying is available in abundance, is easy to hold, can be sold short, and that there are no transaction costs, no taxes and no margin requirements. Where the asset cannot be stored or sold short, the model does not apply as it stands — which is where the expectancy model comes in.

Many fair values, not one. Because borrowing costs and returns differ across participants, the number of fair values of futures can equal the number of participants, and the workbook suggests these differences are part of what keeps the market trading.

Theoretical futures dirty price = Dirty price (A) + Financing cost (B)
Theoretical futures clean price = (A) + (B) − Income on cash position (C)

  A = Clean price + Accrued interest to spot settlement   (30/360)
  B = A × Financing rate × Days to futures settlement ÷ 365
  C = Accrued interest from last coupon to futures settlement (30/360)

The workbook's example. A GOI security with a 5.75% coupon, last interest paid 29 April.

Check the working.

30/360 days, 29 Apr → 4 Aug  = 95   → 5.75 × 95/360  = 1.5174
Financing (B), 23 actual days = 103.0174 × 4% × 23/365 = 0.2597

Theoretical future dirty price = 103.0174 + 0.2597 = 103.2771

30/360 days, 29 Apr → 27 Aug = 118  → 5.75 × 118/360 = 1.8847  (C)

Theoretical future clean price = 103.2771 − 1.8847 = 101.3924

The theoretical futures clean price, Rs 101.3924, is below the cash clean price of Rs 101.5000. The basis is positive (about Rs 0.11) because the bond's 5.75 percent coupon earns more than the 4 percent it costs to finance — the pattern the workbook says bond futures usually show.

If the actual futures traded well above Rs 101.39, a participant could buy the bond, sell the future and lock in the difference — regular arbitrage. Well below, the reverse.

Chapter 3 (Exchange Traded Interest Rate Futures) builds the model in section 3.7: forward rates, financing cost, income on cash position and basis, then section 3.7.2 computes the theoretical bond futures price with the 5.75% GOI example, lists the model's assumptions, and sets up the expectancy model as the alternative in 3.7.3. Chapter 5 (Strategies) uses the theoretical price to explain when regular and reverse arbitrage are possible. Expect a calculation with accrued interest and financing cost, and a question on the model's assumptions.

• Futures price = cash price + financing cost − income on cash position. Income is subtracted, financing added.
• The cash price is the dirty price. Financing is computed on it.
• Accrued interest is 30/360 for G-Secs; financing cost in the example is Actual/365. Mixing the two changes the answer.
• Income on cash position runs to the futures settlement date, not to the trade date.
• Bond futures usually show positive basis (futures below spot), because coupon income exceeds financing cost.
• The model assumes the asset can be stored and sold short, with no costs, taxes or margins. Where that fails, the expectancy model is the alternative.
• There is no single fair value. Different funding costs give different theoretical prices.