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Comment by kruhft | Hacker News Reader

4th year Introduction to Mathematical Finance, but basically 101 in a sense.

Using a binomial model (essentially a random walk) and using 'the formulas' for portfolio calculation, you will find that in the 'long term' (in math, infinite, but 'a long time' in the real world') you will find that no investment portfolio will beat the Prime Rate, as this is what all returns are based off of.

It was just the results I saw from the course. I know one can get 'lucky' and beat the Rate, but overall, as a zero sum game, someone else has to lose and overall the group rate of return is calculated as...the Prime Rate.

Sorry for being condescending sounding; I thought this was common knowledege given it's taught in introductory finance.

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Yeah I don't get why you'd assume 4th year Mathematical Finance would be common knowledge. It still strikes me as knowingly condescending.

I don't agree that someone else has to lose in order to gain. That assumes zero growth, which is not the case.

I think people don't know what you're talking about because you seem to just be repeating stuff you heard in a lecture hall 10 years ago when the world is vastly more complicated.

The stuff taught in introductory finance is a considerably simplified model of the real world. The prime rate is I believe the rate banks lend to large corporations and those corporations wouldn't bother borrowing unless they could get a return exceeding those costs.

To price derivatives one uses risk-neutral probabilities, which are different from real-world probabilities. The binomial tree you talk about cannot be used to calculate the expected return. Maybe this was not properly explained in the course you took, or maybe you were not paying attention.

It's really not.

Judging from your mentioning MC and binomial walks, you might be looking at derivative pricing, and be confused by the facts that

- derivatives are zero-net-supply securities, thus they returns are necessarily zero-sum (minus the exchange/bank's cut)

- derivatives can be priced using the risk neutral measure (after a change of measure, Girsanov's theorem, yada yada yada) in which mu, the drift of all risky assets, equals r, the risk-free rate. However, that's not statement about how mu is in the real world, but basically an abbreviation for an arbitrage-by-replication argument.

At any rate, derivatives pricing is the domain of arbitrage pricing models, while here we are looking at equilibrium models (which consider investors' preferences/utility, unlike arb models).

The linked paper is empirical counterevidence to that theoretical model though.

Admittedly, we can always just say "we're not in the long run," I'm not sure how useful that is.

I'm not certain what model exactly you're talking about, but I think it also probably misses technological change as a real source of growth independent of any monetary musings.

Theory is an 'efficient' market model. Practice is not. Reminds me of the old joke:

An Efficient Market Theorist sees a $100 lying on the ground, and passes it by saying "If that existed, someone else would have picked it up by now!".

> An Efficient Market Theorist

Milton Friedman, in the apocryphal story. And back in my days it was $20 :-)

The paper's data set is from 1870 to 2015, which is 145 years. If that's not close enough to "the long run" for the theory to match reality, then the theory is either wrong or useless.

the sp500 is not zero sum. you are ignoring dividends, and I think stock buy backs throws a monkey wrench into that assumption as well. lastly, population and economy increases.

Haven't taken a mathematical finance course... What is the long-term historical value of the prime rate?

I've seen data showing the overall stock market returns 3% after taxes and inflation for any period longer than about 20 years.

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