An investor buys a non-dividend paying stock for $100 at the beginning of the year with 50% initial margin. At the end of the year, the stock price is $95. Deflation of 2% occured during the year. Which of the following return measures for this investment will be greatest?
A) Real Return
B) Nominal Return
C) Leveraged Return
Can someone explain why this is real return? I thought the real return takes out inflation/deflation. What if the question used inflation instead of deflation? Below is the answer…
No calculations are needed. The real return is greater than the nominal return because the inflation rate is negative. The leveraged return is more negative than the nominal return because the investment lost value and leverage magnifies the loss.
You are correct in the fact that real return takes out the effects of inflation, however think about the formula. If the nomianl rate you receive is 5% per year and inflation is 3% per year you get the real rate of return by 5-3=2%. So in this situation you have the nominal rate minus a negative number which then makes it addition instead of subtraction. I think you’re just over thinking the math on this one.
FIrst let’s look at the relationship between nominal and leveraged returns. Because you’re levered up to half the value of the investment, your actual investment is $50 rather than $100. So, since the % return is the dollar return divided by the initial investment, the levered return will be twice the magnitude of the nominal return. In this case, the calculating a return on a base of $50 will be twice whatever the return is on a base of $100. Let’s assume that the end-of-year price was $90 so, the nominal return would be -10/100 = -0.10 and the levered return would be -10/50 = -0.20. If the end-of year price was $110, the nominal and levered returns would be 10% and 20%. In other words, leverage magnifies both positive and negative returns.
Next, let’s look at the relations between nominal and real return. I don;t hav a calculator with me, so I’ll just approximate. Recall that the nominal return is approximately equal to the real return plus inflation. Or alternately, the real return is the nominal return less inflation. Deflation is “negative inflation”.
So, if the nominal return was -10%, the real return would be -10% - (-2%) = -8%. So, in a world with deflation, the real return is GREATER than the nominal, and in a world with inflation, the real return is LESS than the nominal.
So, from (1), since it’s a negative return, Levered < Nominal;
From (2) Nominal < Real.
Putting it together, Levered < Nominal < Real
Note: This relationship isn;t a general one. The important thing is to understand the two relations individually - Nominal vs Levered, and nominal vs real.