Just in general with these questions. They are all asked the same way and I keep missing. Here;s a sample. An investor buys a stock at 32 a share and deposits 50% margin. Assume the maintenance margin is 25% the stock pays no dividends. Calculate the return on margin if the stock is sold for 37.50 and price at which investor would receive a margin call. ERR Margin Call 17.2% 24.00 17.2% 21.33 34.4% 21.33 34.4% 24.00 Show math please! And a convexity q. IF a bond has a convexity of 60 and a modified duration of 10 the convexity adjustment with a 25 basis point interest rate decline would be: -2.875 -2.125 -.0375 .0375 Thanks
- 34.4%; 21.33 Calc = (37.5-16)/16 Solve for P: (P*1-16)/P*1=.25 2. .0375 Calc = 60*.0025^2*100
So for the second q, do you even use the modified duration of 10?
The second question has the easiest answer, because you know interest declining means the price must increase. 0.0375 is the only option that indicates a price increase. % in Price = Duration * basis Point (in %) Convexity * basis Point (in %) ^ 2 * 100 = 60 * 0.0025^2 * 100 = 0.0375. The Duration in this formula is Effective Duration & not Modified Duration.
No you don’t use the modified duration of 10 in this problem since they are only asking for the convexity adjustment. If they asked what the total % change of the bond is then you would use it.
For the margin call price part of Q1, you can simply use the formula price(1- im/1- mm).