# Real returns

The book lists three formulas for nominal/real return:

(1+r) = (1+RF) * (1+PP) * (1+RP) (1+rr) = (1+RF) * (1+RP) (1+rr) = (1+r) / (1+PP) Where: r = nominal return RF = risk free return PP = inflation RP = risk premium rr = real return

**Question: Asset Class (Geometric return) Equities (8%)****Corporate bonds (6.5%)****Treasury bills (2.5%)**Inflation (2.1%)

The risk premium for equities is closest to:

I solved with the following formula: (1+r) = (1+RF) * (1+PP) * (1+RP) (1 + 0.08) = (1 + 0.025) * (1 + 0.021) * (1 + RP) 1.08 = 1.0465 * (1 + RP) 1.032 = 1 + RP 3.2% = RP

However, the answer in the book is:

(1+rr) = (1+r) / (1+PP) (1+rr) = (1 + 0.08) * (1 + 0.025)

This doesn’t make much sense to me. According to the a previous problem, r is indeed the nominal return (i.e. 8%) and PP = 2.1%. I’m not sure why the answer is the way it is. Any help would be much appreciated!

Are you saying the answer they’re providing you in the book comes out to be 1.08*1.025 - 1 = 10.7% as the Equity Risk Premium?

What answer does the book give, I was having a hard time following

Can you actually give the answer in a number? you formular is division but your example is with multiplicaiton.

However if the answer is 5.4% then I think it is correct, since the equity risk premium is the premium for investing in equity over holding risk free asset, which is T-bill.

Therefore ERP = (1 + 0.08) / (1+0.025) - 1 = 0.054

Both equity and T-bills are in nominal term, thus Inflation is irrelevant

The answer is 5.4%. Sorry for forgetting to include it!

(Sort of) understood. I can rewrite an equation to get (1+rr) / (1+RF) = 1+RP and everything makes sense save for the real rate of return = 8%, the nominal rate as stated in the book.

You rewrote it correctly. The exact equation depends on what the question is asking you for. They ask you for equity risk premium, and it is assumed to be in nominal term (unless stated otherwise). Therefore, use T-bill (nominal term) and equity return (nominal term) then no need for inflation.

If they give you: real risk free rate (let say the same 2.5%), then you do (1+r) = (1 + 0.08) / [(1 + 0.025) x (1+ 0.021)]

Corporate bond is not relevant in calculating equity risk premium (well not until Level 2, when they teach about bond yield plus risk premium approach)

I know that it is a bit confusing at first, but if you get a understanding of what each rate means and WHY they want to calcualate in for the real life application, the remembering will come much easier.