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By looking at Fama and Frenchs global Portfolios, they just use the USD-RF rate as the risk free rate, because they converted their Returns to US-Dollar. Im currently estimating Strategy Returns in emerging markets and now im looking for an appropriate risk free rate.

Since the default risk of foreign treasury bonds is way higher than the risk of US-bonds i don't think that this would be a good approach

So there are two ways i guess:

Is it possible to convert the risk free rate from the US to another currency by using the spot rate/forward rate or expected inflation (hard to get data)

Shall i just convert my Returns into US-Dollar by using the daily/monthly spot rate ?

I think the second approach would be the best, but, since i'm using data streams returnindex:

Can i just convert Datastreams return index from Yen to US-Dollar?

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The short answer us that the risk-free curve that you seek is simply the yield curve of the government bonds denominated in local fiat currency. (Nominal, not inflation-adjusted.) It is extremely unusual for governments to default on such bonds (I know of only two recent examples, Russia and Peru in the 1990s). The government can just print more currency to pay off its debt. That will, of course, cause inflation. The yields observed in the market include the market's inflation expectation.

A longer answer is that a foreign country (emerging, frontier, developed) can have a long list of other observable curves. If the government issues bonds denominated in a currency that is not theirs to print at will, such as the US dollar, the Euro, or sterling, then indeed these bonds are credit-risky. If you use fx forwards, they will include the cross-currency basis (from the difference in the cost of funding in different currencies). You may or may not need that here. Finding an inflation-adjusted (real) curve is hard in many EM countries because there aren't observable liquid inflation instruments, but many research piblishera publish some estimate that are not tradable.

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There is no such thing as a risk free rate. That is an abstract academic construct to keep their models as simple as possible.

In practice, many treat the USD t-bill rate as "the risk free rate". It isn't actually risk free (eg current t-bill interest rates, even before taxes, are below CPI -- so a t-bill buyer faces a lot of inflation risk). If one intends to hold a basket of stocks for 5 years (as an example), then the 5yr Treasury rate might be a more appropriate "risk free" rate than the 3mo T-bill.

Economic models are tools used to help understand the real world, which is more complex than a simple academic model can handle. There are LOTS of assumptions made in economic models to keep things as simple as possible.

If you are buying emerging market stocks, what is the lowest risk alternative? Not "risk free", because there is no such thing. Probably not USD t-bills, because they don't reflect what is happening in emerging markets. Whatever you choose, it will never be "risk free" because there is no such thing.

In emerging markets, 0% might be most appropriate -- as in stash your cash "under your mattress" (or some secret hiding place). It earns 0%, but faces limited risk of capital loss. Note that holding USD cash (instead of local depreciating cash) is still getting 0%.

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How you define things should mirror how you invest/trade. In practice, nothing is 100% risk-free. What people call risk-free rate is really what they'd earn if they don't allocate capital away from their risk-neutral position.

For the vast majority of US investors, this risk-neutral position is simply USD cash, which earns T-bill rates or some USD deposit rates. If an asset, such as EM equities, offers an attractive risk-adjusted excess return, you'd move away from the cash position to earn the excess return by taking on extra risk, and the return will be converted back into USD terms (with FX risk hedged or unhedged). This is the perspective typically taken by academic papers (e.g., Fama/French, DMS, etc.), which is why you see them using USD-converted returns and USD cash return for computing metrics such as Sharpe ratio.

It's also plausible that your risk-neutral position is a long-term bond (e.g., if your investment objective involves liability matching and your liabilities are of super long duration in nature), in which case something like a 30-year bond yield would be a more suitable "risk-free" rate.

Similar principles apply if you're outside the US. Let's say you're in Argentina and you're considering Argentine stocks as an investment option. The question is still what's risk neutral for you if you're not investing in stocks? If it's holding Argentine peso, then whatever rate you'll earn on the cash is the baseline.

Bottomline is that there's no reason to be dogmatic. Use whatever is suitable for your circumstances.

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The least bad answer would be to use local-currency bond yields. But good luck trying. Local issuance in any real size is a relative novelty of the last decade or so. There's no guarantee there's always a nice clean 10 year note live for every country, like a Treasury, Bund, JGB, Gilt etc.; and no guarantee that if it did exist 20 years ago that it was a veyr liquid instrument with reliable signals that people assume from Tsys et al.

Of course, these rates will be (almost) risk-free in local currency terms; but the currency itself is hardly "risk-free" ;-) I say almost because I recall Russia defaulting on local paper in 1998. Probably a few others I've missed, but the defaults on local are definitely outliers. Hey, Germany and Japan defaulted too on the DM side of the ledger.

Whatever the theoretical niceties, using local is always better than trying to use EMBI/$ paper, for which there is a genuine credit risk. Meanwhile, trying to keep everything in dollars and matching vs Tsys/T-Bills is all well and good, but it requires you to dollarise future earnings on the equity side. Good luck forecasting with confidence where BRL, ZAR or TRY will be in 10 year's time ;-) Absent such forecasts, using currency forwards as the obvious naive default is simply equivalent to using local rates.

So the problem you'll get trying to use this data is the nominal public-vs-real private "mismatch". Many years ago, I used to be a stockmarket strategist and we built a suite of models to try to estimate the equity risk premium of different markets. For us, Italy was always the bugbear... because it was quite normal for Italian stocks to exhibit a negative risk premium for prolonged periods of time. It's hard to torture a PE of 10x against a bond yield of 14% and get any different answer. But it's very hard to explain to a client or banker, who just needs an intuitive model input they can sell to their own client.

The short answer is that the ERP was negative! The BTPs were riskless in Lira. Investors were guaranteed their coupon and principal. The yield compensated them for the inflationary risk of getting their principal back in Lira, with an uncertain purchasing power given Rome's fiscal predilictions. Italian stock did have bankruptcy risk. However, these were real assets, measured against a nominal bond yield. Tank the Lira, and their Lira value rises. The negative ERP was simply telling us that the ITL inflation/deval risks were greater than the risks to long-term real earnings. It was safer to own risky factories than riskless paper in a dangerous currency.

With ~5% real rates seen recently in the likes of Brazil, I'd be amazed if you didn't experience similar issues with applying this kind of model to EM.

If's there no way to sanitize your interest rate baseline to make it intuitive and comparable to what the textbooks teach about the US, then Ockham's Razor suggests using zero, and just looking at absolute returns. If these fluctuate as wildly as the inflationary histories of the countries in question, then your equity model is probably mis-specified in the first place.

hope this helps

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