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  1. 079An Indian investor holds a US stock that rises 8% in dollars over a year, while the rupee weakens 5% against the dollar. What is the investor's return in rupees?Currency and global returnsWarm upGlobal investingIndian wealth management

    Try it first

    Pick the rupee return.

    Show the worked solution

    About 13.4% in rupees. The stock turns each dollar into 1.08 dollars, and each dollar now buys 5% more rupees, so each rupee invested becomes 1.08 x 1.05, or 1.134 rupees. The extra 0.4% over simple addition is the currency gain earned on the stock gain.

    Does a weaker rupee help or hurt this investor?

    A student in India whose parents send a fixed dollar allowance from abroad is better off when the rupee weakens: the same dollars convert into more rupees. An Indian investor holding dollar assets is in the student's position, so a weaker rupee adds to the return. Say the direction first, because half the candidates who get this wrong get the sign wrong, not the arithmetic.

    Currency moves compound with the local return; they do not just add+8.0%Stock, in dollars+5.0%Rupee weakens 5%+0.4%Cross term13.4%Rupee return1.08 x 1.05 = 1.134The cross termis the 5% currencygain earned on the8% stock gain:0.08 x 0.05= 0.4%
    The stock's 8% dollar gain and the rupee's 5% fall add to 13%, and the extra 0.4% comes from the currency gain applying to the grown dollar amount, taking the rupee return to 13.4%.

    Where does the extra 0.4% come from?

    Follow Rs 100. At the start it buys a dollar amount; a year later that amount has grown 8%. The 5% currency gain is earned on the grown amount, not the original one, so the currency also earns 5% on the 8% profit, which is 0.4%. For small moves the cross term hardly matters; for a 30% stock gain with a 10% currency move it is 3 points.

    The relationship
    1+rRs=(1+r$)(1+rFX)=1.08×1.05=1.1341 + r_{Rs} = (1 + r_{\$})(1 + r_{FX}) = 1.08 \times 1.05 = 1.134
    r_$the stock's return in dollars, 8%
    r_FXthe change in rupees per dollar, 5%
    r_Rsthe return measured in rupees
    What it says in wordsThe home currency return is the local return compounded with the currency return.

    Run it the other way as a check. If the rupee had strengthened 5% instead, the return would be 1.08 x 0.95, less one, which is 2.6%: a good stock year mostly erased by currency. That is why global allocations report returns in both currencies.

    Where candidates lose it

    The costly slip is the sign: treating a weaker rupee as a loss and answering 3%. It shows the candidate is thinking about the rupee's health rather than about which currency the investor owns.

    The smaller slip is 13% from simple addition. Say 13.4%, and name the cross term, so the interviewer hears that you know returns multiply.

    What the interviewer asks next

    • What if the rupee strengthens 5% instead?
    • How would the investor hedge the currency, and what would that cost or earn?
    • Over ten years, why might currency matter more than the one-year cross term suggests?