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Old 01-28-2003, 04:40 PM
Lucid Lucid is offline
Join Date: Aug 2002
Posts: 33
Default Interest rate concepts

I've noticed an interesting (to me at least) difference in the way professor's in my university's college of business treat a couple of interest concepts, as compared to the way they are treated in actuarial science (i.e. Kellison's Interest Theory and exam 2), and I was wondering if anyone who has been out in the world of actuarial science beyond academia had any comments on them.

First, my business professors have no respect for the discount rate. They treat the discount rate as an unfortunate concept left over from the old days before calculators when financial people would quote bond rates as a rate of discount because it was easier to divide by the par value (almost always $1000) than whatever the bond was actually selling for. So they only talk about the discount rate as an "approximation" for the actual yield to maturity. However, Kellison presents the discount rate as a completely legitimate concept, which is seperate from (although related to) the interest rate (i.e. d = i/(1+i) and such...). The discount rate is not an approximation, but a seperate and equally valid way of measuring interest.

Second, my business professors tend to refer to any effective annual rate of interest as "simple interest", even if the interest is being compounded, I guess because you don't have to worry about compounding within the year, since it is quoted as an annual rate. I'm used to using the term "simple interest" only when it is never compounded.

Does what I'm saying make sense to anyone else? Has anyone else noticed similar differences between business people and mathematical "interest theory" people? I've also noticed differences in annuity terminology (they say "ordinary annuity" instead of "annuity immediate").
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Old 01-28-2003, 06:27 PM
Tri4Ben Tri4Ben is offline
Join Date: Jan 2002
Posts: 364

I have two comments,

1) Business professors are hella lame.

2) College business majors are hella lame.

The professors know that if they start talking about the difference between rate of discount and rate of interest, or the difference between the interest rate and the yeild, nobody is going to have any clue without studying. Since students would rather complain about things being "to hard" than study, professors eventually give in and dumb down the material enough so that the hella lame students can pass the tests.
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Old 01-28-2003, 09:20 PM
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discount rate -- the term is applied to bonds (Course 6) and other various situations (Course 2). I'd tend to agree with their bond-equivalent-yield thoughts - bad math made popular because it's easy not because it's right. But it is nonetheless very prevalent in investment circles and worth knowing. Discount rate, in the Course 2 sense, is used all the time. Most notably, it turns up when calculating loan interest when the loan interest is charged at the beginning of the year rather than the end of the year (interest in advance), which is how loans on universal life contracts are most frequently set up.

Simple interest -- I'd never use the term that way. To me, simple interest means dividend the nominal interest rate by 365 and multiplying it by the number of days to get the total interest, i.e. I = r * days/365, where r=nominal interest rate. For an effective annual interest rate however, 1+I = (1+r)^(days/365). Different calculation altogether. But then again I'd also say nobody other than a middle school teacher would actually use the simple interest concept I described.
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Old 01-29-2003, 01:29 PM
Andy Lang Andy Lang is offline
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Posts: 768
Default Fire your teacher--and Bader and Gold too!

Any teacher purporting to teach you all about compound interest that does not know that the 'discount rate' is merely the reciprocal of the compound interest function, (1+i)^n, should be summarily fired.

Not only is this the backbone of much of what you will do as an actuary, but it also is commonly used throughout the business and financial worlds too.

You cannot properly evaluate ANY long term business arrangement without understading both concepts and that also includes pensions, level premium whole life insurance and even how to evaluate things like nuclear power plants, in which you have huge upfront costs, downstream income and maintenance expenses, and the huge decomissioning costs (often left out or minimized to make the 'numbers work'.

You cannot learn how to invest properly for the long term or how much to pay for a company or a piece of a company without it.

If you want an example of why so many actuaries are floundering, along with the profession, check out the writings of folks like Jeremy Gold and Larry Bader, or the article in this month's Risks And Rewards by Bader in which he makes a pathetic case for investing solely in bonds for a pension fund, presumeably because of the tax advantages.

How this can overtake a differential of more than 500 basis points, Bader seems to leave out.

As I have said before, I have made more money in stocks over my lifettime than I have as salary, and I was VERY well paid in my career.

It also helped immensely in helping pay for my three kids college educations--all private schools, the last the very expensive Stanford University. Yes, I have invested also in other things, including bonds--and an 18.5% zero coupon 'junk' bond paid for half that Stanford education, but that was a very unusual situation and time--unlikely ever to be seen again.

The first thing one should learn in compound interest is that 'interest' is not just bonds but total returns, or 'opportunity costs' or any number of other things--and if more actuaries had mastered it's multiple meanings they would have solved the 'cash balance' thing long long ago, and if more had mastered the historical returns for basic asset classe, they wouod see right away that you cannot get there from here iof all you have is bond returns or heaven help us all, T-bill returns.

Using compound interest correctly will show that there is only one way to provide an accrued benefit in a DB pension plan that will not screw early leaver mployees and it sure as hell ain't by crediting hypothetical accounts with say 5% of pay and then compounding those by T-Bill rates.

Einstein once said that compound interest was the greatest force in the world and Ben Franklin also said that a penny saved is TWO pennies earned, cause he also knew about the power of compound interest long before Albert did.

The reciprocal is just as powertful. How else would your ever judge whether to take a lump sum or 20 payments of $X dollars each for 20 years?
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Old 01-29-2003, 02:04 PM
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NoName NoName is offline
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Andy, you can get a refresher on interest theory, including the term "rate of discount", from many sites, such as

This is a separate concept from the discount rate in the sense that you are using it. Lucid even included the formula in his original post, but you were apparently too busy preparing yet another diatribe about how everyone else in the world besides you is an idiot to notice.
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Old 01-29-2003, 04:22 PM
Andy Lang Andy Lang is offline
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Default Diatribes are highly regarded: why do they ask me for help?

That it IS a separate rate from the sense tha I am using it--and all actuaries should be using it--it is EXACTLY the point.

PS: I am well aware of how it otherwise can being used--like in bond discount rates--and this is something I recall using way back in 1961 when I first became an actuarial student. It is NOT a very useful concept for actuaries or for most business people.

As I said, try buying a business like say an insurance company, without it.
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Old 01-29-2003, 05:39 PM
Emily Emily is offline
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Default Re: Fire your teacher--and Bader and Gold too!

Originally Posted by Andy Lang
Any teacher purporting to teach you all about compound interest that does not know that the 'discount rate' is merely the reciprocal of the compound interest function, (1+i)^n, should be summarily fired.
Does anyone use the term 'discount rate' in this manner? Should everyone be fired? How about 'interest rate'? Is that (1+i)^n? Why don't you just make a whole new language? Personally, I prefer the term 'discount operator' to refer to (1+i)^-n. But that's my language.
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Old 01-30-2003, 04:28 PM
WQN WQN is offline
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Posts: 220

Lucid, you've just learned the lesson that business professors / other college professors have no idea what goes on in the real world, that's why they hide in academia. (The majority of them anyway).
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Old 01-31-2003, 09:33 AM
Andy Lang Andy Lang is offline
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Default LOL


LOL--you just took the words out of my mouth.

One of the reasons why actuaries are so behind the times is that they have relied on academics to teach actuarial science. The book that replaced the old part 4--the classic by Jordan on Life Contingencies--is a perfect example--as are the papers on investing. the latter are mich too heavy on the mathematics and way to lean on both Graham and dodd fundamentals, along with the idea that emotion, and greed, often drives markets in the short term, while profits--real profists not those phony Enron/Anderson profits--drive it in the long term.

It is one thing to understand the math part of investing, another to understand that this math depends heavily on the assumptions and there are also large standard deviations built in.

The latter is NOT a reason for not understanding the math, but for understanding that judgement is and always will be needed--but if you do both, you can make a lot of dough--in the long term, naturally.
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