R30 : V4, P132~137 R40 : V5, P292~295 V4, P132~137 specifically addressed the issue of “hedging of the currency risk of international bond investing (hedging by Forward Contract)”, while V5, P292~295 addressed the issue of “hedging of the currency risk of international investings (applicable for both stock & bond, but hedging by Futures Contract)” and basically the reults shall be same, hedging either by Forward or by Futures), I found that there are some differences in their statements (equations) which confused me much. In V4, on P135, it is said that the Unhedged Return (in domestic currency) = Foreign Bond Return in local currency plus currency return (approximately). The Unhedged Return shall be measued in domestic currency and here, I think, currency return = (St - So) / So. Then, Fully Hedged Return = Foreign Bond Return in local currency plus forward premium or discount. Here, forward premium or discount = (F - So) / So (see P133), here F shall be Fo. On the other hand, on P294, it showed that the (Fully) Hedged Return = Unhedged return measured in domestic currency + (Fo- Ft) / So, here hedge ratio = 1 for Fully Hedging, as shown in equation (4). My questions : Why the Fully Hedged Returns are measured in fifferent ways ? If return measured in local currency and currency movements are same, shall they (both ways ) have same (fully hedged) results ? Is there any difference between hedging foreign bond investment and hedging foreign stock investment ? Your clarification will be much appreciated !
It seems that it is different to hedge foreign investments by Forwards and Futures after my reviewing the contents in both the readings of R30 & R40. However, I do not know exactly what are the differences and why they are different ! Can anyone clear up my confusions ?
There is no difference in theory whether you hedge by forwards or futures. I remember there is a chapter discussing the practicality of using forwards vs using futures. The difference in formula has to do with whether you intend to hold the forwards/futures until expiration. If you do, the formula to use is (F-So)/So. In this case, you lock your exchange rate (of the principal) to the forwards/futures rate. However, if you intend to unhedge in the middle of the contract by settling the outstanding contracts (or just want to calculate the hypothetical return at middle of the contract), you use the (F-Ft)/So which means you calculate your gain/loss of the forwards/future contracts by taking the delta of the committed rates and current rates of similar contracts to be expired at the same time.
elcfa, Thanks for your response ! I am sorry that I still have following questions. 1. Why the equations are different ? In R30, using forward Fully Hedged Return = Foreign Bond Return in “local” currency + (F - So) / So. In R40, using futures Fully Hedged Return = Unhedged return in “domestic” currency + (Fo- Ft) / So 2. In case of holding the contract until expiration, futures can not be used ? In my opinion, both can be used as long as the the expiry dates of both futures and forward meet the timing of the cash flow to be hedged. 3. Do you think the major differences are : A. If the exchange rate shall be locked, then forward shall be used and the expiry date of the forward shall match the timing of cash flow to be hedged, as forward can be tailor-made to meet the timing of cash flows but there is no flexibility regarding the exchange rate and the the timing of cash flows once a forward is contracted. B. If the timing of the cash flow to be hedged is uncertain and a flexibility of lifting the contract in the middle of the course is required, then futures shall be used. In this case, the exchange rate is not locked and it depends on the timing of lifting the futures contract. Your further advice is expected ! Thank you so much !
elcfa, My further questions : 1. The (currency) forward (exchange) rates are determined by IRP, is it that the (currency) futures (exchange) rates are also determined by IRP ? 2. A. In R40 (V5, 294), Fully Hedged Return =“Unhedged” Return in DOMESTIC currency+(Fo- Ft)/So – (1) B. Since in R30 (V4, P135), “Unhedged” Return in DOMESTIC currency = Foreign Asset’s Return in LOCAL currency + currency return [(St - So)/So] --(2) C. Then, we shall have [by substitute (2) into (1)] Fully Hedged Return =Foreign Asset’s Return in LOCAL currency +currency return[(St - So)/So] +(Fo- Ft)/So. In this case, both forward and futures are used for hedging the foreign asset. The currency return [(St - So)/So] is from the forward contract and (Fo- Ft)/So is the gain/loss from the futures contract. But it seems strange to use both forward and futures to hedge at the same time. Anything wrong with me ? I am confused !
- Future / Forward are used interchangeably in the curriculum, as far as I know. 2. substituting 2 into 1 would make sense only if both were being used for the same time frame wouldn’t it. Even if you did… as you have… read the next 4-5 sentences … at least according to me they should cancel each other out at the end of the contract. The F0-Ft/So is applicable when the forward / future is expired before end date - and there is a gain loss component on the instrument. Here you are using a market substitute to determine the gain / loss. (St-S0)/S0 - is the gain / loss at the end of the contract. Additionally if you look at the formulae --> (St - S0)/St and (F0 -Ft)/So – should cancel each other out and you would be left with 0. (1 is t - 0 the other is 0 - t, in terms of subscripts). Are you trying to read too much into this? both the readings are written by two separate authors. So what one author calls “UNhedged return in Domestic Currency” is what the other one is called “Foreign Assets return in LOCAL Currency”
cpk123, Thanks for your response ! Before my reviewing other points mentioned by you and come back later, I will like to say that it seems to me the UNhedged return in DOMESTYIC Currency" shall be different from the “Foreign Assets return in LOCAL (FORIGN) Currency”. Am I wrong ? Maybe I think too much, but these issues confused me much and I will like to clarify them ! Thanks again !
V4: R30, p135 Unhedged Return=Return of foreign bond in Local currency + Currency Return = (Vt - V0)/S0 + (St-So)/S0 Currency Return=Change in Spot Rate (St-S0)/S0 (St and S0 are in direct terms - Domestic/Foreign hence give you the return as a percentage. V5: R40, P294 Hedged Return = R* - rf R* = Return of the Foreign bond in Domestic Currency Terms (and is the unhedged return) =(VtSt - V0So)/VoSo – numerator and denominator cancel out - just a simple number (or percentage) Rf = Change in Futures prices = (Ft - F0)/S0 [Ft, F0, S0 are in DC/FC terms]. Numerator and denominator units cancel out - is just a plain number / percentage. As far as I can see both are the same. Just terminology is different, as the perspectives considered are slightly different. In R40 - they want to emphasize that the principal could change as well as the exchange rate could change. Hence they calculate everything in terms of the domestic currency. In the R30 - they say that the “cross product” does not matter - it is usually small. So they do everything in terms of the Foreign (Local) currency. Also Rh = R* - Rf (The R40 version) so R* = Rh + rf = Rh + (Ft-F0)/S0 same structure without modifying the t and 0 subscripts.
cpk123 Wrote: ------------------------------------------------------- > V4: R30, p135 > Unhedged Return=Return of foreign bond in Local currency + Currency Return > = (Vt - V0)/S0 + (St-So)/So. Is it that exchange rate (So) is not involved in the calculation of the “Return of foreign bond in Local currency” ? It is the return purely measured in “LOCAL (FOREIGN)” currency. For example, if you are a USA investor and you have an investment in UK’s bond with an initial investment (at T=0) of USD12,000.- when the spot rate was 1 pound=1.50USD, so your investment in UK was 8,000 pounds. If the investment in UK has grown to 8,800 pounds (at T=t) when when the spot rate is 1 pound=1.60USD, then the “Return of foreign bond in LOCAL(FOREIGN) currency of POUND” shall be [(8,800-8,000)/8,000]-1=10.0%. The (spot) exchange rate is not involved in the calculation of the “Return of foreign bond in Local currency” at all up to this point. The Currency Return here shall be : [(1.60-1.50)/1.50]-1 = 6.7%, so the approximated Unhedged Return = 10.00%+6.7%=16.7%. Precisely, Unhedged Return=[(8,800x1.60-8,000x1.50/8,000x1.50]-1=17.3% or [(8,800/8,000)x(1.60/1.50)-1=17.3%. In Rh = R* - Rf (The R40 version), so Fully Hedged Return (in DOMESTIC cuurncy) = Unhedged Return - Rf = Return of foreign bond in Local currency + (St-So)/So-(Ft- Fo)/So = 17.3% (in above case) - (Ft- Fo)/So, since Unhedged Return = Return of foreign bond in Local currency + Currency Return, and Currency Return=(St-So)/So and Rf = (Ft- Fo)/So. So, is it correct that : Fully Hedged Return (in DOMESTIC cuurncy) = Return of foreign bond in Local currency+(St-So)/So-(Ft- Fo)/So ? On the other hand, I don’t think that (St-So)/So and (Ft- Fo)/So should cancel each other out (as you said) since the numerators are spot rates and futures rates respectively and spot rate at T=0 and T=t shall be different from the futures rate at T= 0 and T= t respectively. Maybe it is wrong to use both the forward and futures to hedge a single foreign asset at the same time. In summary and in my opinion, maybe forward and futures have different applications, depends on if a fixed rate shall be locked or not (in this case,forward shall be used and the expiry date of the forward shall match the timing of cash flow to be hedged) and if the contract will be lifted or not in the middle of the course before expiration (in this case, futures shall be used and it is not necessarily that the expiry date of the futures shall match the timing of cash flow to be hedged), even though theoretically they can be used interchangebly. Any further comment will be appreciated ! elcfa : would you please give me your advice ! Thanks !
First some math I always find the local vs. domestic wording confusing, so here I use USD for the investor’s currency and Foreign for the other currency. 1. Unhedged return: USD return = Foreign return + currency return = Foreign return + (St– So)/So + Foreign return* (St– So)/So ~ Foreign return + (St– So)/So 2. Fully hedged return: Hedged USD return = [unhedged USD return] + gain/loss in hedging in USD = [unhedged USD return] – (Ft– Fo) / So = ~ [Foreign return + (St– So)/So]– (Ft– Fo) / So In particular: At expiration, Ft = St (i.e., the current forward rate of a contract to be expired must be equal the current spot rate), so Hedged USD return at expiration is approx. foreign return + (Fo– So)/So In summary, hedged return = USD return + (Fo– Ft) / So and is approx. foreign return + (Fo– So)/So at expiration --> both the two authors are correct. Now, there is NO THEORETICAL difference between hedging by futures or by forward. Whether you use forward or futures is of practical reasons. Forwards is a private arrangement (typical between a bank and a company/investor) while futures is regulated/traded in an exchange. Using forwards is more flexible (expiration date, privacy, currency coupling…) but a bit more risky (since a bank can default), more cumbersome (paperwork, contract to be signed) more expensive while using futures is less flexible (standard expiration, standard currency coupling, less privacy,…) but less risky, a bit cheaper and be traded very quickly. Your argument about difficulty to cancel a forward contract is not correct. You can exit a forward contract quite easily but entering into an opposite contract using current forward rate thus in effect cancelling both contracts out. Lastly, a bit of advice. Level III is more about synthesis of material, so I would advice you to “pull up” a bit to see the overall pictures instead of burrowing yourself into the nitty gritty details and get confused since you don’t understand the key things first, or as they say: “Seeing the Forest, Not Just the Trees”. Not saying that you should not focus on the details. In fact, you MUST do that but do it AFTER you have seen the BIG picture and understand how to apply the basic principles.
i just hit this section and it’s break time. trying to finish SS10 and jam through quite a bit of SS11 this weekend. Fixed Income is no joke in L3. whoever said this stuff is back-weighted, grr… i forgot but it’s so true. finish this and i get to derivs and attribution? wow, feb and march look awesome. i’m back though. it’s feb. time to get serious.
elcfa…since it appears that you have mastered this topic how would you apply these formulas to Question 8 of page 325 reading 40? Thanks for you help
elcfa Wrote: ------------------------------------------------------- > 2. Fully hedged return: > Hedged USD return = [unhedged USD return] + gain/loss in hedging in USD > = [unhedged USD return]–(Ft– Fo)/So = ~ [Foreign return+(St–So)/So]–(Ft– Fo)/So > > In particular: At expiration, Ft = St (i.e., the current forward rate of a contract to be > expired must be equal the current spot rate), so Hedged USD return at expiration is > approx. foreign return + (Fo– So)/So > > In summary, hedged return = USD return + (Fo– Ft)/So and is approx. foreign return + > (Fo– So)/So at expiration --> both the two authors are correct. > > Now, there is NO THEORETICAL difference between hedging by futures or by forward. > Whether you use forward or futures is of practical reasons. > > Your argument about difficulty to cancel a forward contract is not correct. You can exit a > forward contract quite easily but entering into an opposite contract using current > forward rate thus in effect cancelling both contracts out. Great ! My confusions are fully relieved by your explanations ! > Lastly, a bit of advice. Level III is more about synthesis of material, so I would advice > you to “pull up” a bit to see the overall pictures instead of burrowing yourself into the > nitty gritty details and get confused since you don’t understand the key things first, or > as they say: “Seeing the Forest, Not Just the Trees”. Not saying that you should not > focus on the details. In fact, you MUST do that but do it AFTER you have seen the BIG > picture and understand how to apply the basic principles. Thank you very much for your advice ! Reviewing some old exams and according to some charterholders as well as those who passed the L3 exams, it seems that the Trees (rather than the Forest) were examed more intensively. Actually, I am seeking to integrate the knowledges incorporated in L3 curriculum. This is my main purpose in pursuing the “CFA”, not just pass the exams. By the way, would you please kindly take a look at my other messages posted on this forum ? I sincerely hope that you can give me some advices regarding the questions raised by me. Thank again !
elcfa…since it appears that you have mastered this topic how would you apply these formulas to Question 8 of page 325 reading 40? Thanks for you help
AMA I think I’ll take a pass. Don’t think I have enough time for your numerous and lengthy questions. If I see if any can be answered quickly, I may. Intelo: I assume you are referring to the HFS Trustees case. If correct, you can’t, not directly anyway. The formulas I have written is about calculating the ACTUAL return of hedged/unhedged portfolio, while the case asks about whether you should or should not hedge based on your EXPECTED return. In directly, you can use them in the following way: If your expectation is correct, your unhedged return is = Foreign return + (St– So)/So = Foreign return + (1/80 – 1/100)/(1/100) = Foreign return + 2.04% Note that the author uses indirect quote convention while the example gives direct quote. Your hedged return (at expiration) is ~ foreign return + (Fo– So)/So where (Fo– So)/So is the forward premium as calculated in the answer to be 5.16% using IRP equation so Your hedged return (at expiration) is Foreign return +5.16% Hedged return is thus higher than unhedged return.
Thanks elcfa…that is precisely the source of my confusion…The way I understood the question was that you can leave the return unhedged in which i case I get what you have, mainly, Return unhedged = Foreign return + (St– So)/So = foreign return + 2.04% Now using the Hedged return formula we get Return Hedged = Return Unhedged - Rf. But Rf = -5.16%, so one should not hedged. Essentially, per the book if you hedge, then if the foreign currency depreciates, you benefit from your hedged position by getting - - Rf = +Rf. But if the currency appreciates then you also get the downside - Rf. however, given your explanation above and just reviewing my notes again, I guess I was viewing the forward premium as Rf since that is what is used to hedge throughout the chapter. The investor is comparing what she thinks the return (s) will be ie 2% to what interest rate parity is implying it will be (5%). So this is a different kind of hedging they are referring to here, as opposed to using futures. When you look at all of their examples where the futures are used to hedge, they go with the assumption that IRP holds and the basis (interest differential) is zero, which is not the case in Question 8. Thanks for your help on this
and btw, for what it’s worth, Question 8 is a direct application of the currency section in R30 as opposed to R40. I dont know why they put it under R40. Lesson here is to think about the problem as opposed to try to apply what you just read in the chapter.
Intelo I think you misread both the text and my comments. You need to read very carefully what I wrote. 1. I imply that they SHOULD hedge since hedged return is higher which is the same as CFAI answer. 2. You seem to be confused. You used Return Hedged = Return Unhedged - Rf and Rf = -5.16%, but it is wrong. Chapter 40 uses Rf to indicate the return of the hedge, NOT forward premium as you indicate here. It also uses the USD Unhedged return instead of Unhedged in FOREIGN currency formula you indicated. In short, You MUST use, ie. = [unhedged USD return] – (Ft– Fo) / So, where unhedged USD return = Foreign return + 2.04% and Rf = (Ft– Fo) / So is NOT the forward premium (i.e 5.16% as you wrote), but = the CHANGE OF FORWARD in relation to Spot = gain/loss of the hedge in USD currency. In this case, Ft = St = 1/98. So= 1/100. Fo= as given in the answer = (1+ 5.16%)* So so gain from hedge = - Rf = - [1/98 - (1+ 5.16%)*1/100]/ 1/100 = 3.12% Check: USD hedged return (at expiration) = USD unhedged return + return from hedge = (foreign return + 2.04% )+ 3.12% = foreign return + 5.16% as I wrote above. 3. In final conclusion, there is NO difference between this hedge and hedging using futures. As I said earlier, there is NO theoretical difference in using forward vs. future.
elcfa Wrote: ------------------------------------------------------- > AMA > > I think I’ll take a pass. Don’t think I have enough time for your numerous and lengthy > questions. If I see if any can be answered quickly, I may. Of course, only if you have enough time. Your any response to my other messages posted on this forum will be very very much appreciated !