Hello, I calculated this using 0.05*-20%+0.05*0.95*(0.6^0.5-1)+0.05*0.95^2*(0.4^(1/3)-1)+0.95^3*i=0.1. Why does this not work? Thank you
It's not clear what you've done here. If the Examiners' Report is unclear, check out the ASET for a full explanation.
I have used the ASET but I feel as though this should work. I have annualised the returns from each of the outcomes and multiplied by the probability of their occurrence. For example, when the bank can get 8000 back in the first year if the customer defaults they have made a return of -20% annualised. For the second year the bank can get back 6000 at the end of year 2 which works out as 0.6^0.5-1=-22.54%. Then the same for the return in the 3rd year given a default and finally the annualised return required in the event of no default is i. I have then set this equal to 10% which is the expected return required. I feel like this should work, as I said, can you explain why it does not?
Oh, I see what you mean. I think that your approach misses out the time value of the payments. For example, whilst it may be true that there's a probability of 0.05 of receiving an annualised return of -20%, that only applies for one year. The 0.05*0.95 probability of achieving -22.54%, whilst annualised, is actually realised over two year. Therefore the expectation you've performed doesn't quite cover it.
Hi, It is clear that in the examiners reports they have calculated the present value, so all values are at time 1 to calculate the return required. When I first attempted this question, I calculated it all at time 3 instead. (0.05*8000*1.1)+(6000*1.1^2*0.95*0.05)+(4000*1.1^2*0.95*0.95*0.05)+(10000*1.1^3*0.95^3) and set this equal to 10000*1.1^3 However, I can't think of how we would account for the desired expected return in the method I am using.
Hi, If you used an approach as at time 3, you would have the same formula as in the Examiners' Report but multiplied by 1.1^3 (so the answer for the annual rate of interest will be the same). The desired expected return (10%) is applied to the sale amounts of the car on default to make it as at time 3 (eg the first term would be multiplied by 1.1^2, not 1.1 to go from year 1 to year 3). If there is no default after 3 years 10000 is repaid increased by the annual rate of interest for 3 years. As you say, you would then set this equal to 10000*1.1^3 .
