hedging via futures

wen we hedge an all equity portfolio via futures, making its beta=0, what is our earning in case the markets go up by 10%? do we earn risk-free rate of return? plz provide a proof with d help of nos.

Never thought about this. Would it not depend on the movement of the future rate price? Still waiting for an answer from someone else.

Think of equity return as the sum of the risk free return and and equity risk premium. By hedging, you eliminate the additional riskiness of equities, which is reflected in the equity risk premium. So, although it does not mean that your return will be the risk free return, your benchmark has to be it.

With a perfect hedge i.e. with no basis differential , you will earn the risk free rate. Roughly F=S*e^t. The e^t part is the return component by investing S amount in the commodity . So intuitively , by borrow S dollars at the risk free rate and investing in the short futures contract ( I know , I know that futures does not require up front investment , but the notional amount is supposedly invested in T-Bills , so it earns the risk free rate ), The futures price represent a future value of the S dollars at the risk free rate over time t

take dis problem, i cant solve it… UK fund invest 200m pounds into US stocks with a beta of 2.5. Initial exchange rate \$1.5/ pound, investment horizon-3 months. Exchange rate after 3 months \$1.6/ pound. Rf in US= 6% p.a., Rf in UK= 4% p.a. 3month S&P index= \$1200, after 3 months they quote at \$1320. Initially, S&P futures quote at= 1200*1.06^0.25= \$1217.61. This investment exposes the UK fund to market as well as currency risk. Assume that S&P has gone up by 10%. Can you tell me what happens when the fund decides to hedge market risk via futures with beta of the portfolio=0? Theoritically, whenever an investment is made in foreign currency market and hedging is done, it will earn the foreign currency risk-free return, but i cant seem to prove it. Plz help.

nasty problem. wouldn’t even attempt on exam, wastes too much time.

kanupriya_newatia Wrote: ------------------------------------------------------- > take dis problem, i cant solve it… > UK fund invest 200m pounds into US stocks with a > beta of 2.5. Initial exchange rate \$1.5/ pound, > investment horizon-3 months. Exchange rate after 3 > months \$1.6/ pound. Rf in US= 6% p.a., Rf in UK= > 4% p.a. > 3month S&P index= \$1200, after 3 months they quote > at \$1320. Initially, S&P futures quote at= > 1200*1.06^0.25= \$1217.61. > This investment exposes the UK fund to market as > well as currency risk. Assume that S&P has gone up > by 10%. Can you tell me what happens when the fund > decides to hedge market risk via futures with beta > of the portfolio=0? Theoritically, whenever an > investment is made in foreign currency market and > hedging is done, it will earn the foreign currency > risk-free return, but i cant seem to prove it. > Plz help. What is the implied Beta of the Future? Otherwise I cannot solve it.

kanupriya_newatia Wrote: ------------------------------------------------------- > take dis problem, i cant solve it… > UK fund invest 200m pounds into US stocks with a > beta of 2.5. Initial exchange rate \$1.5/ pound, > investment horizon-3 months. Exchange rate after 3 > months \$1.6/ pound. Rf in US= 6% p.a., Rf in UK= > 4% p.a. > 3month S&P index= \$1200, after 3 months they quote > at \$1320. Initially, S&P futures quote at= > 1200*1.06^0.25= \$1217.61. > This investment exposes the UK fund to market as > well as currency risk. Assume that S&P has gone up > by 10%. Can you tell me what happens when the fund > decides to hedge market risk via futures with beta > of the portfolio=0? Theoritically, whenever an > investment is made in foreign currency market and > hedging is done, it will earn the foreign currency > risk-free return, but i cant seem to prove it. > Plz help. I don’t think it will be exactly the risk free rate because you cannot perfectly hedge equities. The value of the asset at a future date is unknown.

No. It is pretty much the RFR. There is CFAI problem that proves it. In the problem posted, the implied beta of the future is missing. Cannot calculate the # of fut to sell. Please provide.

I think you can calculate # of futures to sell = [(0 - 2.5) / 1] * [300 million USD / (1217.6 * 250)]. This of course assumes that the S&P index has beta of 1, which is probably incorrect (most likely 0.98 or something around there). 300 million is from 200 mn pounds * 1.5 exchange rate, and I multiply by 250 as that is the S&P multiplier (also assumed). Hence, this is why I wouldn’t even attempt this question on the real exam, as there are so many variables that are subject to question that any error in a number throws everything else off. F that.

Believe me if you give S&P a beta of 1.0 , you would be ok. Don’t split hairs on that one.

mik82 Wrote: ------------------------------------------------------- > No. It is pretty much the RFR. There is CFAI > problem that proves it. In the problem posted, the > implied beta of the future is missing. Cannot > calculate the # of fut to sell. Please provide. Can you reference this problem? I’m hesitant on agreeing with this statement because there are examples where you have to calculate the effective beta. If the hedge was perfect, then effective beta would always equal the target beta.

BTW I also searched the book for the term “risk free” and came up with no hits.

#1 This is a morning session type question so you have to look for the key word/action word (I can’t remember what they are called). Nowhere in this question does it say Solve, or Calculate. I say proving this on the test is not necessary and I would doubt that CFAI would even ask this question as one needing a calc or quantitative solution. however, if they did, I agree with the above that more information would be needed if this was not a perfect hedge. Also, I would doubt that they would have you assume the beta on the S&P future as 1. #2 stepping back from a quantitative view on this question and just looking at the qualitative aspects of it you see it is meerly asking if you are a foreign investor that hedges the market risk only in your foreign portion of the portfolio, what risks are left? The answer clearly is that only currency risk remains and you earn the foreign currency Rfr and the change in value of the foreign currency for the length of time you are hedged. #3 Now that we know what return we would be getting calculating that is easy (well easier than trying to factor in the futures position with everthing else) so the foreign curr Rfr is 6%/4 = 1.5% and curr return is -6.25%(in GBP invested in USD terms) over the 3 month time frame so total return would be a loss of 4.75% However I maintain that this question, for maximum points, does not need a calculation. The qualitative explanation in #2 should be enough, and #3 is just bonus information.