Nature of Competition: Rate of Return

 

For the purpose of illustration, we herein calculate some rates of return. Particularly in conjunction with financial instruments, the term “interest rate” is used in place of “rate of return.” In either name, the current price and the (expected) rate are inversely related, ceteris paribus.

 

My house on the hill. Suppose my house in the rental market. I rationally believe that the residential service is valuable at $100 per annum “in real” “in the long run.” On the other hand, I set the value of time as 2% PA. Again, the value of time is as real as the time is. This is as opposed to that the “time value of money” in finance is "nominal."

Question 1: What price would I sell the house outright in the asset market at? The answer of rationality is “the PV” (for present value) of the cash inflows in the undefined run of future. Unfortunately or rather fortunately, PV is not as straightforward to calculate as it appears to: there is the “risk factor” particularly in the discipline of finance.

            Fortunately, we are in economics and might idealize all the “risk factor” away. And, undefined, indefinite and limitless are close cousins in science. Now, we mobilize algebra for the sake of calculation convenience; specifically we go for the indefinite geometric progression.

             He-----er’s the PV= $5,000 = (100/ 1.02) + (100/1.02²) + (100/1.02³) + ……. Now in the asset market (as opposed to the rental market), I am at the margin of $5,000 (as regards the question to sell or not to sell).

Question 2: I successfully sell the house at $5,000 and make a deposit of the same amount at 2% PA with my bank even more credible than the Fed. How much interest would I get at the end each, of all the coming years in the long run?

             That’s even easier: $100 per annum, in real and free of risk, not to mention

Question 3: In the short run, the asset price is no less fickle than the mind of B. Dreamer’s boyfriend. Suppose the price of the house goes up to $10,000 one time and falls down to $2,500 another time. On the flipside, the cash inflows in the rental market would not vary because they are “in the long run” of trend. What would be the rate of return respectively?   

            Here are the answers: the rate of return is 1% PA in the one time; the same is 4% PA the other time. A great discovery, the price of an asset and the rate of return is inversely proportional. In reality, however, as each and every asset has its own expiry, the two are inversely related, shorter than “proportional.”

 

Additional investment and the return. Suppose I expend $5,000 for the purpose of Home Improvement. I wouldn’t do that for fun; but I am very purposive and duly expect an additional rental income per annum of $100. Not to mention, the price of my house will in the long run be fluctuating around $10,000 in real. Hereby, we double-confirm that the price and the rate of return are inversely proportional to each other.

             An interesting inquiry: What is the most consistent across markets but the least steady over the time? Thinking rationally at the margin, the candidates are: the price, the rental income, the rate of return, the mood of B. Dreamer, the mind of her boyfriend, the hypothesis of researcher, the opinion of journal editor, the policy of central banker and the spirit of gamblers.

Fixed-income security. There in the reality are such things as “fixed-income securities.” Suppose a perpetuity bond issued by the US Treasury which pays $100 per annum in nominal. If anyone buys a unit of bond at $5000, the rate of return or the interest rate is 2% PA in the name only.

             Here again, we find the inverse proportionality between the (spot) price and the (expected) rate of return. Incidentally, will the annual income out of the perpetual Treasury be fixed? Yes, we are conjectured to believe so. No, “the only fixed is variable,” if history is any guide. Heard of Pax Romana?

 

“Market force.” The short run price of the asset is fluctuating. Nevertheless, the so-called “market force” will keep trying to hold the price around the PV which is the only fair and rational price. Nice try, but: Particularly in the short run, the invisible interest rate is as fickle as the inscrutable sprits of animal.

             Alas, Science is one, Technology is another, and Engineering is still another. On the sidewalk, Mathematics is always expediently smiling as King the Convenient. Economics is Science at least, while monetary policy is Engineering at most. 

Home Improvement (1991–1999)