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1. It is known that at the maturity it is imperative that there needs to be convergence between the spot price and the future price. Based on the risk free rate of 6.32% p.a, the future price of WBC share on March 6 can be estimated in the following manner.

Maturity date of the WBC future as given in the question = 27th April

Hence,  days to maturity = 27th April -6th March = 52 days

Spot price of the WBC share on March 6 = \$ 27

Continuous compounding is being assumed for the calcualtion of the future price in the given case

Let the future price of WBC on March 6 be denoted as Fo

Fo = 27*e0.0632*(52/365) = \$ 27.244

Hence, the difference between the future price and spot price on March 6 = 27.244 – 27 = \$ 0.244

Now, if the spot price of the WBC stock is 27.50 then, Fo = (27.5)*e0.0632*(52/365) = \$ 27.749

Thus, the revised difference between the future price and spot price = 27.749 – 27.5 = \$ 0.249

From the above calculation, it can be derived that as the spot price of share would increase, the theoretical deviation between the future price and spot price should increase as indicated above.

2. Ideally, the future price should be equivalent to the value as computed above. However, in case of any deviation from the above price, there could be arbitrage opportunities which can be exploited by an adept trader. The trading strategy would essentially depend on whether the future price is above or below the expected price. Also, the strategy discussed below assumes that the cost of trading is zero.

Spot price of WBC = \$ 27.5 and Future price > 27.749

In the above case, let us assume that the price of the WBC future expiring on April 27 is \$ 28.5. Hence, in order to earn profit through arbitrage, a trader should borrow funds to buy the stock the WBC stock at \$ 27.5 and enter into a futures contract whereby he/she would sell the WBC stock at the end of April 27 for \$ 28.5.

Total cost to the trader = \$ 27.5 + interest cost = 27.5 + 0.249 = \$ 27.75

Total benefit to the trader = \$ 28.5

Hence, arbitrage profit = 28.5 - 27.75 = \$ 0.75

## Calculation of Future Price and Spot Price

Spot price of WBC = \$ 27.5 and Future price < 27.749

In the above case, let us assume that the price of the WBC future expiring on April 27 is \$ 26.5. Hence, in order to earn profit through arbitrage, a trader should short sell the WBC stock at \$ 27.5 and enter into a futures contract whereby he/she would buy the WBC stock at the end of April 27 for \$ 26.5.

Total cost to the trader = \$ 26.5 + interest cost = 26.5 + 0.249 = \$ 26.75

Total benefit to the trader = \$ 27.5

Hence, arbitrage profit = 27.5 – 26.75 = \$ 0.75

It is given that the cost of trading is 6.5 cents per share or \$0.065 for both stock and future since one lot of future is equivalent of one share. Hence, the total cost of trading involved in both buying and selling = 0.065*2 = \$ 0.13

Thus, this cost would erode the arbitrage profit of the trader and hence arbitrage strategy as explained above should be implemented only if the deviation from the fair price for the future is more than \$ 0.13 in either direction. If the deviation of the future price from the fair price is less than \$ 0.13, then no arbitrage opportunity exist. However, in order to maximise the arbitrage profit, another method is to increase the volume per transaction which would reduce the transaction costs and hence would ensure that opportunities for arbitrage profits are maximised. Based on the exact size of the trade, the range and extent of arbitrage profits can be determined.

Part 2

Introduction

Arbitrage is referred to as risk free profit earning opportunities that are presented for a brief period of time. With the advancement of technology, there is a greater emphasis than ever to run complex algorithms to identify the opportunities for arbitrage and execute the same usually through automatic consoles run by powerful computer. In this background, the aim of this report is to analyse the presence of arbitrage opportunities and underlying strategies to execute the same on the trading session on March 6. Further, in case of presence of arbitrage opportunities, the underlying profit from the trades is calculated while in the absence of arbitrage opportunities, the reason for the absence would be explained. Besides, the report also contains a brief overview of the enabling factors responsible for the presence of the arbitrage opportunity. This analysis has been done based on the trades executed on the stocks of WBC stock and its future expiring on April 27.

Factors for presence of arbitrage

In order for arbitrage opportunity to exist, one of the following conditions need to be fulfilled.

• The law of one price is not obeyed i.e. the asset does not trade at the same price in different markets.

• There are two assets that have exactly same cash flows but still do not trade at the same price which gives rise to arbitrage opportunity by buying undervalued asset and selling the overvalued asset.

• The asset with a definite future value tends to deviate from its future price after discounting using the risk free interest rate.

In the given case, since the stock and its future is under consideration, hence for arbitrage opportunities to exist, the pricing of futures of WBC shares should deviate from their expected value.

Existence or Absence of arbitrage opportunities

In order to evaluate the existence or absence of arbitrage opportunities in the trading session on March 6, the approach was to ascertain whether the value of futures indeed is equal to the expected value or not. For the estimation of expected future price, it is assumed that the interest is compounded on a continuous basis.  Also, the risk free rate in the given case is taken to be 6.32%.

Days to maturity of the future contract = 27th April - 6th March = 52 days

Let the spot price of the underlying stock on March 6th be equal to S0

Then, the expected future price Fo = S0*e0.0632*(52/365)

The various trades that were executed on March 6th are summarised below.

 type security time stamp Price volume seller buyer trade WBC 52:02.0 25.16 2 sim uowuno20 trade WBC 54:07.5 25.17 2 sim uowuno20 trade WBC 56:51.5 25.19 1 sim uowuno20 trade BCJ7 51:41.1 25.24 2 uowuno20 sim trade BCJ7 54:25.3 25.32 2 uowuno20 sim trade BCJ7 56:59.5 25.37 1 uowuno20 sim

It is apparent from the above that the WBC stock is being bought while the WBC futures are being sold at the same time. The underlying rationale is that the futures are overpriced which is not justified by the formula stated above. Hence, trade has been initiated on the assumption that arbitrage profit can be made. In order to test this claim, the expected future price for the three trades can be found out and compared with the actual price of the futures at that moment as shown below.

When S0 = \$ 25.16, then Fo = 25.16* e0.0632*(52/365) = \$ 25.39

When S0 = \$ 25.17, then Fo = 25.17* e0.0632*(52/365) = \$ 25.40

When S0 = \$ 25.19, then Fo = 25.19* e0.0632*(52/365) = \$ 25.42

It is apparent from the above calculations that there were surely arbitrage opportunities since the futures seem to be underpriced. However, in the given case the arbitrage opportunity has not been reaped as is apparent from the following section.

In the given case, the stock has been purchased at spot price and the futures have been sold.

Total units bought = 5

Total unit sold = 5

Total cost = Spot price of WBC shares + Interest cost = 25.16*2 +25.17*2 + 25.19 + (25.39-25.16)*2 + (25.40 – 25.17)*2 + (25.42 – 25.19) = \$ 127

Total benefits from sale of futures = 25.24*2 + 25.32*2 + 25.37*1 = \$ 126.49

Total loss = 127-126.49 = \$ 0.51

Hence, in the given case there has been a loss of 51 cents on account of the transactions that have been enacted with regards to WBC stocks and their respective futures.

To consider the impact of the trading cost on the overall profit, we would first need to correct the strategy so as to make a profit. In order to make an arbitrage profit, we need to buy the underpriced future contracts for WBC and sell the spot WBC stock. In this transaction, the cost benefit analysis would be as shown below.

Total cost for purchasing the futures = 25.24*2 + 25.32*2 + 25.37*1 = \$ 126.49

Total benefit from selling the WBC stock in spot market = 25.16*2 +25.17*2 + 25.19 + (25.39-25.16)*2 + (25.40 – 25.17)*2 + (25.42 – 25.19) = \$ 127

Hence, total profit = 127 – 126.49 = \$ 0.51

Since there are in total six transactions that have been done, hence the total transaction cost based on the cost of 6.5 cents per transaction = 6.5*6 = 39 cents or \$ 0.39

Thus, net profit after deducting the transaction costs = \$0.51 - \$ 0.39 = \$ 0.12

Hence, in case of transaction costs, the trade size also becomes a critical parameter and the volumes need to increase so as to minimise the impact of the trading cost on the arbitrage profit. The higher volumes would ensure that the transaction cost per unit stock would be minimal and hence sizable profits could still be made. However, if the transaction is limited to a single stock, then the arbitrage opportunity would be significantly impaired.

It is apparent that my trading strategy did not actually yield arbitrage profits even though there were such opportunities which presented themselves during the trading session. However, perhaps the overall concept of arbitrage especially in a practical scenario needs some more practice. Additional factor which was an issue was the small time frame within which the trade had to be executed as the arbitrage margin is typically very thin and usually limited to a few cents only. In such a case, it is imperative that trade must be executed in a blink of an eye or else the price may change. This situation tends to be demanding especially on a first time trader like me who tends to get panicky. Therefore, it is imperative for the future that I do more practice of exploiting such arbitrage opportunities on the relevant simulation platform before implementing the same in actuality. Further, the usage of various calculating aids is quite critical for identification of the underlying deviation which in turn dictates the strategy for earning arbitrage profits. Besides, detailed analysis and understanding needs to be performed on the subject so as to consider looking into advanced concepts such as dynamic arbitrage.

Conclusion

On the basis of the above discussion, it may be concluded that the given trading session did present arbitrage opportunities since the future prices did not confer to the expected future prices. These opportunities were identified through calculation of expected future price based on the given expiry date and the prevailing spot price. In the given case, the futures were underpriced and the arbitrage strategy should have been to buy the underpriced futures while selling an equivalent amount of the WBC stock in the spot market. However, due to lack of practical exposure of trading in a challenging environment coupled with shortage of time frame of trade execution, the actual strategy implemented in this case resulting in loss instead of arbitrage profit. In the event that the trading costs are also considered, the arbitrage profits would come down and also the opportunity for the same may also take a dip. However, one solution to ensure that the arbitrage profits continue to remain is to enhance the volume per transaction so as to lower the overall cost per share. The performance in the future can be improved by enhancing familiarity and experience of trading in a time crunch situation along with the underlying theoretical concepts which need to be absolutely clear so as to be able to excel in a real time trading environment. The stakes in arbitrage transactions are often high especially because in such transactions the volume size is high so that even a small profit per share could develop into sizable gains.

Cite This Work

[Accessed 15 July 2024].