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

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=Se^rt(assuming no income)=100e^0.1(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).

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