After taking a basic Mathematical Finance course, you'll find that nothing does better than the Prime Rate in the long term, unless you get lucky, or unlucky.
unless we are talking about two different things (what is the best thing to invest in to get the most returns over the long run), either you missed interpreted what the course was trying to teach you or its just factually wrong.
I took historic data from 1950 till now and matched it with the prime rate. I even gave you the benefit of the doubt by taking the max prime rate of the given year.
even if you invested at the peak of the dotcom bubble in 1999, you would have done better (100$=>255$ vs 246$)
* for optimal portfolios: more risk -> more return
* however, idiosyncratic risk of a security doesn't matter (as it can be diversified away)
* what matters is systemic risk, ie correlation with the market return (or state of the economy): something that is negatively correlated (ie protects you by returning higher returns in a bad economy) is worth more, thus has lower returns
Individuals can, but overall, the net gains by all players is the risk free rate.
I’ll give you a hint that may open your eyes. Volatility is not risk.
It was quite a dissapointing result when I learned it.
Anyway models of low risk investments will underestimate long term crashes /Black swan.
Also, are you comparing other assets directly or somehow including combinations of them? Can you point me to a specific theorem you seem to be referring to?
I wish i could find the actual theorem, but it's been a few years since I took the course and have long lost the textbook[1]. It was pretty clear though when it was taught, or at least that's what I gleaned out of that lesson without the teacher having to say it.
[1] https://en.wikipedia.org/wiki/Capital_asset_pricing_model
The risk free rate of return is reduced because people want to leverage short term cash flows. A 99% chance of gaining 5% is not necessarily worth a 1% chance of losing 5%. EX: Collage tuition is paid before teachers salary's are paid, so collages want somewhere to stuff money for a weeks, but losing money is vastly worse than some minor gains.
If you model the stock market by say buying evenly from all stocks and selling in 50 years repeat. Then some outliers like dell at IPO going up 500x more than makes up for losses. But, you can still lose a lot of money over say 5 or even 20 years and people can't necessarily wait 50 years.
E(R_m)-R_f is sometimes known as the market premium (the difference between the expected market rate of return and the risk-free rate of return).
Nothing does better than the prime rate? You mean in terms of interest rate? Isn't the definition of the prime rate the best you can get?
In the long term? What does that even mean here? Can I get lucky and do better than the prime rate, whose definition is the best interest rate you can get?
Saying this knowledge is basic Mathematical Finance is also very condescending. I haven't taken "that course" but I feel from your tone that you took a 101 college course which now guides your entire mode of economic thinking.
Elaborate on your statements.
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.
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.
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!".
Milton Friedman, in the apocryphal story. And back in my days it was $20 :-)
I've seen data showing the overall stock market returns 3% after taxes and inflation for any period longer than about 20 years.
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.
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).