Very Easy Question- That is confusing the Sh*t out of me. I have a share worth $100 that I would like to sell in 1 year? The risk free rate is 5% per year 100 (1.05)^1 = $105 = The no arbitrage price that I would sell the share for. I understand this. CFA text agrees. I enter into a forward contract to sell for $105. I am out- I could also have sold the share now for $100 and bought the risk free rate to get $105 In three months the price of the asset goes down to $90. It does not matter to me I still get my $105. But now the price to buy the share in 9 months (0.75 years) only costs 90 * (1.05)^0.75 = $93.35 The investor has essentially lost 105- 93.35 = $11.65 The CFA text does not agree. They would like to discount $105 back by the risk free rate for 9 months 105/ 1.05^0.75 = $101.22 – 90 = $11.22 The text states that the investor loses $11.22 The equation is 90 – (105/ (1.05^0.75)) In simple English why am I thinking about this incorrectly?
Analyst100 Wrote: ------------------------------------------------------- > Very Easy Question- That is confusing the Sh*t out > of me. > > I have a share worth $100 that I would like to > sell in 1 year? > The risk free rate is 5% per year > > 100 (1.05)^1 = $105 = The no arbitrage price that > I would sell the share for. > I understand this. CFA text agrees. > > I enter into a forward contract to sell for $105. > I am out- You are out, but you haven’t recieved the $105 yet. It won’t be worth that until year end. >I could also have sold the share now for > $100 and bought the risk free rate to get $105 Imagine you did sell the share and bought the risk free. It would be worth 101.22 after .25 years. > > In three months the price of the asset goes down > to $90. > It does not matter to me I still get my $105. > But now the price to buy the share in 9 months > (0.75 years) only costs > 90 * (1.05)^0.75 = $93.35 > > The investor has essentially lost 105- 93.35 = > $11.65 > > The CFA text does not agree. They would like to > discount $105 back by the risk free rate for 9 > months 105/ 1.05^0.75 = $101.22 – 90 = $11.22 > > The text states that the investor loses $11.22 > They are just taking the present value of each position and netting them. You can’t do that with your $105 because it is a future value. > The equation is 90 – (105/ (1.05^0.75)) > > In simple English why am I thinking about this > incorrectly? That is my take.
Another way to look at this would be to draw a time line and try to see when you are recieving the cash flows. 11.65 you mentioned is the loss for the investor at the end of 1 year while 11.22 is the amount lost today. So if you discount, 11.65 by 1.05^0.75 you will get 11.22
Thanks Kabhii. You are correct. I thought about that late last night. Could also be 100* (1.05)^0.25 - 90 = $11.22 The amount that has been lost in the first 3 months.
I’ve made that mistake too. Never forget to discount it back to the pricing date.