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Calculation of Mean and Standard Deviation

 
 
Reply Sun 2 Nov, 2014 05:23 am
Hi Everybody,

Would need some help on this please.

USASuperCars sells luxury sports cars. It has just signed a contract to sell, in a years’ time, a batch of these cars to various customers around the globe. The following table shows the orders of seven customers. The selling prices are fixed and in local currencies at the exchange rate prevailing at the time of the delivery. Of course there is uncertainty in the exchange rates, and in order to cope with this uncertainty estimates, as well as standard deviation of these have been provided by the Bank of America. The report that came with these estimates stated that these rates are normally distributed and independent.
Worldwide Orders Exchange Rate (to $)

Csmr. UK Japan1 Japan2 Canada1 Canada2 S. Africa USA

Qty. 12 5 3 1 3 2 1

Price. UK= £57,500 Japan1=Y 8,400,000 Japan2=Y 9,000,000
Canada1=CAD 97,000 Canada2=CAD 100,000
S.Africa=R 4,100,000 USA=$100,000

Ex.R.Mean 1.401 0.0091 0.0091 0.8248 0.8248 0.0211

Ex.R. SD 0.041 0.00045 0.00045 0.0342 0.0342 0.00083

Q.1. Find the distribution and report the mean and the standard deviation of the total revenue in $
Q.2. If the offer is to pay the sure sum in three months’ time rather than in twelve months’ time, would that make any difference? When would the bank and when the company would prefer the payment to be made, and why?
Q.3. USASuperCars has accepted HSBC’s offer. Now consider the bank’s risk, assuming the bank will convert all currencies into US dollars at the prevailing exchange rates. What is the probability that the bank will incur a loss?
Q.4. The bank defines its Value-at-Risk as the loss that occurs at the 5th percentile of the uncertain revenue (5% left tail of the distribution). What is the bank’s Value-at-Risk and what is the bank’s expected profit?
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