Reference: 2016 SchweserNotes Level III Book 3 - Assigned Reading:18 (Currency Management: An Introduction) - LOS18.h - page 175-176
Strong positive correlation between Rfx and Rfc increases the volatility of Rdc. A hedge ration greater than 1.0 would reduce the volatility of Rdc.
Strong negative correlation between Rfx and Rfc naturally decreases the volatility of Rdc. A hedge ratio less than 1.0 would reduce the volatility of Rdc.
Can anyone help explain the concept and application of MVHR in simple words and the above statements? I dont get the idea behind all of these.
Lets say, for example, Rfx and Rfc are negatively correlated in Japan which is heavily dependent on export. I bought 100 shares at 100JPY and need to convert it back to my USD portfolio after 3 months. So I should literally short JPY10,000 forward, right? But since the hedge ratio is less than 1.0 as Statement 2 says, I should ideally short less than JPY10,000? I dont get it.
If the correlation is negative (not perfectly) then what happens when the shares rise in price? The JPY goes down.
Let’s say the correlation is -0.5, and the shares rise 100%, then the JPY/USD should also rise by 50%.
If you hedge only JPY100,000 forward, you end up with JPY100,000 that are not hedged, of which their return has gone down by 50%. So your total return for the move was return on forward (let’s say -10%) *.5 + -50%*.5 + 100% = 70%
If the correlation was positive, you would find an exaggerated return instead. What you should understand from it is this, if the returns move together, then you should increase the hedge ratio, because you would likely find big moves in either direction, and hedging a bigger portion reduces volatility (and return in absolute value), while underhedging would not as much. And lower the hedge ratio if the correlation is negative, since the volatility is already reduced between the Rfx and Rfc, so overhedging would puts you at risk of higher returns when the stock market returns are positive, since you buy a portion of the FC at the depreciated marktet.
sorry, just want to clarify, Rfx is measured in DC/FC right? Basically it means that if there is a positive relationship between the foreign currency value and the return on foreign asset, then we should use a hedge ratio of greater than 1? For example, when foreign currency appreciates and the foreign asset yields a positive return, a hedge ratio of greated than 1 should be used to reduce the volatility. Correct?
I just saw a statement on another forum saying “For example, if when the local currency appreciates the underlying asset is more likely to appreciate too then you would want to hedge less than the principal amount. I guess the optimal amount will be function of the strength of the relationship.”.
Doesn’t this mean the opposite? “hedge less than the principal amount” = hedge ratio of less than 1?
If you overhedge on a positve correlation, two things can happen (assume fwd rate = spot rate)
Both return postively, you earn the stock market retrun plus minimal fx gain/loss
Both return negatively, you are clearly overhedged in this situation, you lose the stock market return, and gain the remainig principal on the hedge not covered by the stock market proceeds. By changing the DC to FC at a lower rate, and getting it back at the higher fwd rate, or simply sell the contract for a gain.
In both instances, the return volatility is reduced, because they are banded.
Yes, let’s assume MVHR is 0.8 (less than 1 due to negative correlation between Rfx and Rfc), then you should short JPY 8000 = 0.8 x JPY 10000.
The idea being if Rfx and Rfc are negatively correlated, they are effectively hedging each other and reducing the volatility of the portfolio, so you do not need to hedge the full amount of the investment.
It seems like you’re trying to interpret a correlation like a slope, which isn’t correct, even with your assumptions. Correlation can’t tell you how much y changes due to a given change in x. A perfect correlation of +1, for example, doesn’t indicate a 1 to 1 change in the variables.
Granted, I haven’t looked at LIII material, but it does seem like this is the idea you were getting at.
Isn’t the slope of a regression p*sdy/sdx? I’m not saying the correlation is the slope itself (according to your 1 to 1 example, but it’s a variable of the function). The numbers I used in the example were more importantly emphasizing the casual relationship of movement direction, not the magtnitude itself. Again, it was overly simplified obviously.
Yup… I’m still a little confused about the zero error and zero coefficient comment. Would you mind clarifying that?
Ah, I see. In your example, though, the ratio of standard deviations would need to be 1 for the example to work as you made it. I was more concerned about someone reading what you had wrote and confusing the ideas of a slope and a correlation (which is a very common thing to do for people who are just learning). You had a good point, overall, though–movements tend to be in the same (opposite) direction about the respective means if it’s a positive (negative) correlation.
If the regression measured the first order relationship between the two variables, then you need to have a zero coefficent in order for the relationship to hold linearly, and no residual errors (which is implied in regression analysis anyway). The standard deviations need to be equally dispersed, not nessecarily 1, for the slope and correlation to come out equal as well. It would have been more confusing making all these assumptions explicity, while mentioning the correlation alone as per the example would have been sufficent to get the point across.
Which coefficient are you referring to in the model? Would you mind writing out a model to demonstrate that. It still isn’t clear.
Linear regression (OLS) doesn’t imply no errors. It assumes that the average of the errors is zero. Individual predictions can be off, but we get it right, on average.
Good catch. I did mean the ratio of the standard deviations (I corrected my post).
Probably, but it would definitely be sufficient to give someone the wrong idea about interpreting a correlation.
Again, I think it was a good point about the directions and synchrony of movements.