Why is risk:return rarely a 1:1 ratio
Under an ideal world/efficient market, you would assume that for every additional risk that you take, you’ll be compensated an equal amount of return. However, when you look at the historical cagr/std ratios (ignoring risk free rate), you would find that the sharpe ratio is almost always <1 for all passively manages assets in the long run. What are some possible reasons to explain why this is the case in the data? (Ofc I’d assume that if assets with a sharpe >1 exists, that usually would be arbitraged away)?
Based on the most helpful WSO content, here are some reasons why the risk:return ratio is rarely 1:1:
Market Efficiency and Anomalies:
Systematic vs. Idiosyncratic Risk:
Risk Factors:
Behavioral Factors:
Transaction Costs and Market Frictions:
Arbitrage Opportunities:
Passive Investing and Market Efficiency:
Historical Context:
These factors collectively explain why the risk:return ratio is rarely 1:1 in real-world data.
Sources: A Contrarian View - Raging Bull, Reflections from year 4 as an equity analyst, Why do people invest in hedge funds?, Is Anyone Bullish on the Future of Asset Management???, Explain to me like I'm a 12 year old the benefit of a hedge fund
Probability of reward is the key reason.
Can you elaborate a little bit more on that?
As a macro analyst I would think you know this but using really simple logic, in order to have the same expected value of 0 (efficient market), do you think the risk to reward would be the same or different for a gamble/speculation where the probability of winning is 90%, versus a 1%? Obviously you would need a bigger payoff (or risk to reward) for the 1% bet to make it a fair trade against the 99% bet. And before you say markets aren’t perfectly efficient, it’s not the point, the point is just that higher risk/probability of loss requires better risk to reward ratios to be attractive compared to alternatives
So what you're implying is that it's less risky for me to just play Baccarat. Say no more.
At first I thought this was a silly question:
So you’re saying 1% risk exposure requires a 1% return - well then by definition there cannot be risk. There’s no volatility it’s just upward drift at a linear rate. Basically you’re just talking about the risk free rate (which is return / 0 risk).
But the more I thought about the more interesting it becomes. Why is the stochastic discount factor higher than the return in most cases. I’d say it is just a mixture problem and you end up in macroeconomics land. As if you generalise you’re effectively talking about Global GDP growth (I.e. more quantity with less input) vs Global Inflation (I.e. higher prices). When you think of return in a financial sense it’s only one part of the puzzle - is it quantity driven or price drive. Then the idea of what the best types of compensation for “risk” makes more sense. Inventing a new technology that is adopted and subsequently creates true greater productivity (no VC BS about “B2B SAAS”, but like the Car, the Plane, the internet, the steam engine, electricity etc).
In finance land our job is to allocate capital in order to foster greater productivity, not lead to the general inflation of prices (which basically is a misallocation of capital). So to me I see the sharpe ratio point as a natural balancer (highest returns are linked to true productivity gains, not price inflation which is itself fleeting in the long-long-run); things with lower sharpes basically are indicating poorer capital allocation because not every opportunity is one which improves productivity, there’s just a tonne of inflation plays.
final thing I’ll say is that Sharpe doesn’t really get at asymmetry of distributions or kurtosis (fat tails); but the vibe of the point remains - the risk/return ratio should ultimately point to productivity. (You can also link this to the general idea of NPV as well; which is “risk adjusted” “cash flows”).
There’s a tonne of theory im ignoring (risk neutral vs. risk averse investors, inter-temporal rates of substitution etc); but I wanted to try and bit a little bit more novel to see if this point resonates.
Ok but why 1 excess return for 1 point of portfolio deviation? Why not 2? Why not 0.25? What about GDP and inflation empirically centers around 1 as a ceiling?
Well where is that 2% coming from?
....Okay the counterparty
Okay, where does the counterparty get that extra money?
...someone else
And where does that someone get money?
Trace it to the end (where does it magically come from if not Total Factor Productivity? https://en.wikipedia.org/wiki/Total_factor_productivity)
You are assuming that annual cagr and annual std are the quantities that you expect equality from. These are very reasonable and commonly used metrics, but why expect equality from them?
Why not daily cagr and daily std?
Or monthly cagr and average absolute monthly return?
These all lead to different numbers.
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