Question

In: Finance

Assume you have $10mio in investor capital. Show the growth of this capital since the start...

Assume you have $10mio in investor capital. Show the growth of this capital since the start of 2018 assuming you were continuously engaging in a simple arbitrage strategy where you buy the low-priced asset and sell the high-priced asset. Be sure incorporate all the real-world frictions that would arise if you were implementing the arbitrage such as interest rates, storage, insurance, transportation costs, natural disasters, theft, fraud, etc.

Formula 1: F0=S0e(r-q)

where r represents the interest rate, q represents the cash flow yield earned from holding the asset (i.e. dividends), and T is time in years

Formula 2: F0=S0e(r-rb)T

where rb represents the interest rate of the base currency as quoted and r represents the interest rate of the second currency, all continuous compounding.

formula 3: F0=S0e(r+u-y)T

where r represents the interest rate,u represents the storage and/or insurance costs expressed in constant proportion, and y represents the convenience yield

NOTE: THERE IS NO DATA OF R, RB, U, Q AND Y and all are based on assumptions.

1. Describe the forwards/futures pricing model that is appropriate for the asset you select. This could be formulas 1, 2, or 3 above or some variation of these. Hint: Since this market is new, there is no model or approach that is best. I am looking for your intuition.

2. Clearly outline the arbitrage strategy, and show the payoffs for one sample trade. State how large your trades will be, being mindful of the practical limit (i.e. you only have $10mio in capital).

3. Track the growth of your $10mio in the capital since the start of 2018 assuming you were continuously engaging in the strategy. Show your returns by month and for the entire period ending in June.

Start Date 12/31/17
End Date
Spot 3-month futures
XBTUSD Curncy Bid Price Ask Price XBT3 Curncy Bid Price Ask Price
Dates PX_BID PX_ASK Dates PX_BID PX_ASK
1/1/18 13623.3887 13625.7402 1/1/18 14550 14690
1/2/18 14783.1543 14786.0449 1/2/18 14700 15300
1/3/18 15054.3164 15056.1445 1/3/18 14800 15300
1/4/18 14944.75 14947.9492 1/4/18 14700 15220
1/5/18 16751.3262 16755.1406 1/5/18 16830 16890
1/8/18 14933.7012 14937.6855 1/8/18 14760 15240
1/9/18 14546.125 14562.0254 1/9/18 14750 15000
1/10/18 14493.0352 14496.4492 1/10/18 14260 14750
1/11/18 13459.4219 13466.5313 1/11/18 13250 13750
1/12/18 13745.1719 13747.9902 1/12/18 13770 13850
1/15/18 13915.6504 13917.9922 1/15/18 13770 13850
1/16/18 10719.9922 10720 1/16/18 11000 12420
1/17/18 11372.4805 11380.8906 1/17/18 10610 11330
1/18/18 11605 11606 1/18/18 10610 11330
1/19/18 11350 11383.2109 1/19/18 10610 11330
1/22/18 10350 10358 1/22/18 10610 11330
1/23/18 10981.0391 10981.0508 1/23/18 10610 11330
1/24/18 11211.7344 11214.9961 1/24/18 11270 11400
1/25/18 11250.6094 11262.4375 1/25/18 2010 11250
1/26/18 10872.1602 10877.416 1/26/18 10970 11050
1/29/18 11200.0078 11213.9805 1/29/18 11010 13790
1/30/18 10082.0039 10091.5898 1/30/18 9760 10490
1/31/18 9962.3066 9962.3145 1/31/18 10010 10140
2/1/18 9089.4492 9098.957 2/1/18 20 9170
2/2/18 8569.9922 8570 2/2/18 8480 8600
2/5/18 7092.8906 7108.8516 2/5/18 6520 8990
2/6/18 7762.2969 7766.8984 2/6/18 6930 8360
2/7/18 8082.3594 8092.6582 2/7/18 7760 9590
2/8/18 8165.5 8176.8711 2/8/18 7800 8740
2/9/18 8546.0977 8559.1992 2/9/18 8640 8700
2/12/18 8823.5 8839 2/12/18 8610 9590
2/13/18 8556.4414 8559.3711 2/13/18 8510 9590
2/14/18 9285.4414 9290.4805 2/14/18 8820 9590
2/15/18 9865.9023 9881 2/15/18 8550 11990
2/16/18 10082.3984 10094 2/16/18 10200 10240
2/19/18 11077.6406 11085.1719 2/19/18 10200 10240
2/20/18 11700.8086 11710.6406 2/20/18 11760 11950
2/21/18 10282.5898 10291.0977 2/21/18 9060 13540
2/22/18 9915.6797 9915.6914 2/22/18 9810 13540
2/23/18 9920 9920.0117 2/23/18 9810 13540
2/26/18 10375.1719 10385.4297 2/26/18 8550 13540
2/27/18 10744.5977 10767.1992 2/27/18 10730 11220
2/28/18 10533.0391 10543 2/28/18 10410 12040
3/1/18 10927.2969 10940.1992 3/1/18 10400 11310
3/2/18 11025.9922 11033.8984 3/2/18 10400 11310
3/5/18 11555.9805 11555.9922 3/5/18 11400 11900
3/6/18 10787.6992 10793 3/6/18 10520 13550
3/7/18 9936.8086 9942.2422 3/7/18 9570 10800
3/8/18 9327.2617 9333.1992 3/8/18 9060 10300
3/9/18 9004.832 9004.8398 3/9/18 9060 10300
3/12/18 9014.0703 9021.2305 3/12/18 8750 10300
3/13/18 9060.3281 9065.5195 3/13/18 8750 10100
3/14/18 8300 8308.6367 3/14/18 8190 8710
3/15/18 8250.0078 8253.4102 3/15/18 7900 9200
3/16/18 8520.3809 8527.9609 3/16/18 7900 9200
3/19/18 8424.2559 8430.1367 3/19/18 8000 8900
3/20/18 8912.625 8928.0254 3/20/18 8150 9200
3/21/18 8894.2441 8896.9336 3/21/18 8800 9280
3/22/18 8597.5 8600.1914 3/22/18 8110 9280
3/23/18 8611 8621.5 3/23/18 8110 9280
3/26/18 7887.3906 7890.2891 3/26/18 7800 9280
3/27/18 7990.4902 7991.2461 3/27/18 7700 9000
3/28/18 7898.9492 7914.9766 3/28/18 7700 9000
3/29/18 7097.0059 7099.2637 3/29/18 7700 9000
3/30/18 6848.5449 6856.4707 3/30/18 7700 9000
4/2/18 6936.8398 6937.9199 4/2/18 6900 8000
4/3/18 7401 7401.8047 4/3/18 7200 7670
4/4/18 6830.0137 6831.4961 4/4/18 6620 7670
4/5/18 6749.5 6749.6016 4/5/18 6100 7300
4/6/18 6601.8184 6607.1445 4/6/18 6100 7300
4/9/18 6660.4414 6663.834 4/9/18 6600 7300
4/10/18 6838.4746 6840.7598 4/10/18 6600 7200
4/11/18 6889.9453 6892.1152 4/11/18 6830 7200
4/12/18 7730.4453 7730.5 4/12/18 7480 8000
4/13/18 7900.4395 7907.3711 4/13/18 7480 8000
4/16/18 7984.2988 7987.8105 4/16/18 7800 8250
4/17/18 7913.9082 7915.4844 4/17/18 7800 8270
4/18/18 8185.7383 8189.3203 4/18/18 8010 8250
4/19/18 8233.8008 8233.9023 4/19/18 7800 9880
4/20/18 8522.9805 8526.0586 4/20/18 7800 9880
4/23/18 8931.375 8933.1152 4/23/18 7800 9880
4/24/18 9448.5703 9451.1934 4/24/18 9320 9880
4/25/18 9070.1797 9076.1992 4/25/18 8760 9500
4/26/18 9118.9297 9118.9941 4/26/18 8650 9480
4/27/18 8975.9434 8978.1992 4/27/18 8650 9480
4/30/18 9272.3906 9273 4/30/18 9260 9880
5/1/18 9015.3652 9016.0996 5/1/18 8880 9880
5/2/18 9175.5273 9176 5/2/18 8880 9880
5/3/18 9647.3086 9656.7656 5/3/18 9280 9880
5/4/18 9682.3086 9684.7617 5/4/18 9280 9880
5/7/18 9436.2578 9438.9883 5/7/18 9250 10980
5/8/18 9160.75 9161.1953 5/8/18 9020 9700
5/9/18 9245.5449 9250.8398 5/9/18 9100 9700
5/10/18 9091.7422 9093.5977 5/10/18 9100 9395
5/11/18 8432 8432.0117 5/11/18 9100 9395
5/14/18 8810.916 8812.4043 5/14/18 8450 9000
5/15/18 8516.3105 8521.1992 5/15/18 8300 9000
5/16/18 8291.2188 8291.2305 5/16/18 8295 8880
5/17/18 8201.7969 8206.3008 5/17/18 8100 9900
5/18/18 8225.2695 8233.8906 5/18/18 8100 9900
5/21/18 8404.5977 8409.1738 5/21/18 8250 9250
5/22/18 8108.3984 8108.6484 5/22/18 8000 8650
5/23/18 7589.9922 7590 5/23/18 7600 8390
5/24/18 7550 7554.8984 5/24/18 7580 8250
5/25/18 7446.4805 7449.6699 5/25/18 7580 8250
5/28/18 7212.6992 7216.8984 5/28/18 7580 8250
5/29/18 7497.2344 7505.8516 5/29/18 7400 8250
5/30/18 7336.0195 7338.5 5/30/18 7280 7885
5/31/18 7535.9004 7540.666 5/31/18 7280 7885
6/1/18 7436.4922 7438.9883 6/1/18 7280 7885
6/4/18 7522.543 7528.9883 6/4/18 7280 7885
6/5/18 7627.6582 7631.4082 6/5/18 7400 7885
6/6/18 7618.1406 7620.4941 6/6/18 7605 8200
6/7/18 7659.3691 7660.75 6/7/18 7500 8200
6/8/18 7644.5645 7647.9883 6/8/18 7500 8200
6/11/18 6758.0195 6763.7656 6/11/18 6575 7250
6/12/18 6530.4102 6532.3711 6/12/18 6410 6865
6/13/18 6259.1309 6262.7949 6/13/18 6010 6400
6/14/18 6657.9629 6659.5938 6/14/18 6390 7200
6/15/18 6496.6445 6499.3008 6/15/18 6390 7200
6/18/18 6725 6730.1016 6/18/18 6710 7010
6/19/18 6693.0977 6697.7734 6/19/18 6700 7010
6/20/18 6747.3633 6750.416 6/20/18 6500 6880
6/21/18 6719.1289 6719.8008 6/21/18 6660 6880
6/22/18 6067.9492 6072.4375 6/22/18 6660 6880
6/25/18 6250.5195 6251.1016 6/25/18 5980 6700
6/26/18 6243 6243.8672 6/26/18 6240 6280

Solutions

Expert Solution

(1) Formula 1: When the underlying asset for a forward contract pays a continuous dividend, then the forward contract should trade low. Eg: shares and bonds

Formula 2: This equation is used to compute theoritical forward exchange currency price.

Formula 3: If there are both Costs(storage cost) and benefits(lease rates,convenience yield) in buying the commodity today, then the holder is wiiling to accept a lower forward price WRT benefit and higher forward price WRT storage costs.

If the storage cost is more than the benefits, then the theoritical forward price will be greater than spot price and viceversa.

(2) Arbitrage gains exist when theoritical price as per the pricing model doesn't equal to actual price.
Say, commodity spot price(s0)=100, R(interest rate)=10% per annum then the forward price after 1 year as per the pricing model will be F=Sert(assuming no income)=100e0.1(1)=100*1.1052=110.52

If the actual price in 1 year is 115, then there will be a arbitrage profit of 4.48 (buying the commodity now, holding it till maturity and selling it at the price).

jeff jeffy answered 1 year ago
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