For example, if a US domiciled investor has a Japan-based asset, when we calculate the Sharpe ratio, should we use a US risk-free rate or one from Japan? Likewise, if we have a client in Japan for whom we've purchased assets in the UK, which country's risk-free rate should we employ?
In risk-adjusted return measures such as the Sharpe ratio, we use the risk-free return to derive the risk premium (portfolio return minus risk-free return). It's the premium the investor is entitled to, for taking on more risk.
If the portfolio manager picks a Japanese asset, presumably it's because they want to gain exposure to that market. And so, to me, the alternative risk-free asset would be one from Japan.
A challenge arises when we invest in a country (e.g., emerging market) where there is no risk-free asset. In these cases, I would think it reasonable to default to the risk-free asset of the investor's home country. These are views that I've come up with without the benefit of discussion with others, and so I am open to being corrected, enlightened, persuaded to adopt alternative ones.
This is an interesting topic, I believe, that is worthy of much discussion. This is the first time I've opined on it, and am curious what you think, so please offer your comments!
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I would think the rf rate choice would be dictated by the reporting currency. For example, a global portfolio being reported in USD would use a USD denominated rf rate, while the same portfolio being reported in JPY would use a JPY denominated rf rate.
ReplyDeleteDaryl, thanks for your comment.
ReplyDeleteThe base currency of the portfolio whether it is hedged or unhedged. I think this would represent the investor's baseline for risk even if that is not their domestic currency. What currency is the bulk of portfolio's cash balance? (Assuming that small or residual amounts of various foreign currencies are held and the majority of the cash is in the base currency of the portfolio.) The portion of the portfolio that is not fully invested (in cash) would represent what the manager sees as risk free. If that is USD then a dollar rate, if that EU then a euro rate,...
ReplyDeleteAlthough we generally avoid posting from "Anonymous," I made an exception here ... thanks for your input
ReplyDeleteThe answer is the investor's home currency risk-free rate. This is the only solution that is consistent with the definition and the performance applications you cite. The investor can avoid risk by investing in the home currency cash option, or take on an variety of risks, each having their own reward for the volatility that they contribute relative to that domestic risk-free option. This has two implications: the returns of all risk investments must be restated to the investor's base currency; and the volatility and correlation statistics are then calculated from that return stream in base currency.
ReplyDeleteOnce again, the answer lies within the question: "What is the risk TO THE INVESTOR of investing in a risky asset?" Currency risk is one of these, and it's effects are reflected in returns stated in the investor's home currency. The risk-free rate must be consistent with these definitions.
So, when would you use the local currency risk-free rate? When you are answering this question for a local currency investor. It's really the same answer. But remember, we are analyzing this investment in the context of a specific investor, and not in a vacuum.
I appreciate your response, which seems to be quite definite, with no chance of flexibility, which is fine. You and I had a conversation regarding the appropriate risk free rate to use for bond investments, and I thought you felt that the yield curve should be of the local investment, which would conflict with this. I don't agree with that case, as I believe that the foreign bonds would be priced relative to its own yield curve, not necessarily that of the home currency. I agree that we must think about what the question is. If the investor is investing in, for example, Germany, they have the option of investing in a risk-free asset or an asset with risk; I would think then there could be an argument for using the German risk free asset. I am trying to be completely open about this, and sincerely do appreciate all of the input. I am unaware of any source(s) to refer to, though think this is an interesting conversation and topic.
ReplyDelete