Talk:Real interest rate

To all Users: Caveat Emptor
Twice I have tried to get Mr Newberry's comments on issues I have with this page. He has refused both times, and twice rudely erased my input to replace his own. He clearly thinks this is his own personal page. He doesn't need to be correct. Retail Investor 21:13, 18 September 2006 (UTC)

Things I have changed
I have deleted the following because taxes are not part of the subject. "This simple definition is much more complicated in practice. For example, if the recipient of the interest has to pay income tax, it is usually levied on the nominal interest rate, and so the tax rate will also affect the real interest rate. "

I have rewritten the following to make it more understandable. "The real interest rate is the nominal interest rate minus the inflation rate. It is a better measure of the return that a lender receives (or the cost to the borrower) because it takes into account the fact that the value of money changes due to inflation over the course of the loan period.  This distinction is particularly important in periods when inflation is high, and is more likely to be ignored when inflation is low (e.g., under 2 percent)." Retail Investor 00:35, 8 September 2006 (UTC)

Dear Stirling Newberry

 * Before I use the revert process, I'll say what my problem is with your input. The factors you specify for compensation by interest, all apply to all interest.  They would be correctly detailed on the page "Interest rate".  This page is a sub-set of the bigger set.  The whole point of this subset is not the factors that remain included... the point is the factor that is excluded = inflation.  Nobody wanting to find out what factors can be charged out as interest will search for "real interest rate".  They will search "interest rate".


 * I agree that to explain what 'real' interest is, you have to explain what nominal interest is, but I did that clearly and concisely. I am trying to do some housecleaning here.


 * As far as your statements the 'real' interest rates require a "currency adjustment" and an "adjustment for compounding" : I can't see where you got that thought.  Can you explain?  (yes, I do understand what each of those are)

Retail Investor 16:15, 9 September 2006 (UTC)

To be technically correct
Since inflation 'works' upon real rates, the relationship is multiplactive, not additive. E.g. if inflation is 2% and nominal interest is 5%, the real rate is not (5-2=)3%. It is 2.941%.

$$\$1 \left( 1+real\% \right) \left( 1+inflation\% \right) = \left( \$1+nominal\% \right)$$ $$\$1 \left( 1+2.941\% \right) \left( 1+2\% \right) = \$1.05\% $$

Retail Investor 16:20, 26 September 2006 (UTC)

$$ \,\! r_{nom} = \left( 1 + r_{real} \right) \left( 1 + i \right) - 1 \approx r_{real} + i $$, where $$r_{nom}$$ is the nominal risk-free rate, $$r_{real}$$ is the real risk-free rate, and $$i$$ is the expected inflation rate.

Hi, I believe in the third paragraph where it states, "Conversely, when the real rate of interest is low, demand will move from savings to investment and consumption." It should read; Conversely, when the real rate of interest is low, demand will move from savings and investment to consumption. Chris. — Preceding unsigned comment added by 87.101.223.130 (talk) 11:16, 17 November 2012 (UTC)

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The investor rationally should not expect to get the real interest rate after allowing for inflation
The first passage currently reads, that the "real interest rate is the rate of interest an investor [...] expects to receive after allowing for inflation".

I don't think that the real interest rate, as it is currently defined, can be seen as the rate of interest that someone can probabilistically expect to receive after allowing for inflation (or as I say: "in real terms").

With Jensen's inequality: E[f(I)] is not necessarily the same as f(E[I]).

Example:

Let I be a random variable for the inflation rate with the realizations I=0.1, I=0.8 and I=0.6 all equally likely. Let r_nominal = 0.1. Then according to the definition of the real interest rate here, the result is: E[I]=0.8 and r_real = (1+0.1)/(1+0.8)-1 = 0.0185.

However, the actual expected value of the real interest rate given the same information above is actually: E[R_real] = E[ E[R_real|I]] given by the law of iterated expectation. Therefore the result is: 1/3*0 + 1/3*0.0185+1/3*0.0377 = 0.0188.

I've roundet to three decimals but the difference between 0.0185 and 0.0188 is not due to rounding errors but due to Jensen's inequality. The real interest rate in presence of random inflation is defined with respect to the expectation value of the random inflation rate and the nominal interest rate. But it is not equal to the expectation of the real interest rate.

Therefore the investor rationally should not expect to get the real interest rate (i.e. 0.0185), as it is defined here, after allowing for inflation. The investor should expect to get the expected real interest rate (i.e. 0.0188) after allowing for inflation.

Best regards. 2003:D8:9F2A:100:7DCC:9195:2F10:E50C (talk) 01:32, 23 May 2024 (UTC)