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> Sharpe ratios and all those “risk” adjusted calculations all involve assumptions that may or may not be true. On the contrary, these risk adjusted measures a

> Sharpe ratios and all those “risk” adjusted calculations all involve assumptions that may or may not be true. On the contrary, these risk adjusted measures assume nothing more than a normally distributed random variable. If you just look at annualized returns, then go ahead and invest in CDOs ETFs. More seriously, the S&P for instance has around 20% annualized vol, which IMHO is way above what you would want for a retirement fund. I would target something closer to 10%. > Comparisons of just annualized returns over long periods of time seems fine for broad market index funds Do you have any sort of reasoning or is it just a gut feeling?

g15jv2dp 2y ago
> On the contrary, these risk adjusted measures assume nothing more than a normally distributed random variable. The financial sector isn't yet so unrelated to reality that the price of securities is random.
- Galanwe 2y ago
  I think when stating your opinion against 40 years of econometrical research, including multiple Nobel prizes in economy, you should feel enticed to explain your opinion a bit more than "no I don't think so"...
  - Maxatar 2y ago
    This is absolutely absurd. Economists including Nobel prize winners, including even Eugene Fama who proposed the Efficient Market Hypothesis, does not think the stock market is normally distributed. At best, using a normal distribution is something that undergrads use as a tool to learn about the stock market and make some simplifying assumptions for pedagogical purposes, but it most certainly is not something that actual professionals or researchers in the field genuinely believe.
    - Galanwe 2y ago
      Come on, don't create a trial of nitpicking. I am not saying returns are a law of nature meant to teach us normality. My point is that, for all intent and purposes, you should assume normal distribution of returns. If you don't, you're obviously on either end of the spectrum: not knowing the subject at all, or nitpicking expertise on the internet. The subject of the matter here is convincing someone that risk adjusted measures should be considered when comparing portfolios. This is the basic underlying modelisation that 99.99% of the finance world makes, "compare sharpes", "compare volatility adjusted returns". I'm stating 1+1=2 and you're arguing it doesn't hold in Z/2. > At best, using a normal distribution is something that undergrads use as a tool to learn about the stock market and make some simplifying assumptions for pedagogical purposes Implicit normality assumptions are everywhere. I encourage you to think hardly about your model and question whether anything you do would work on non normal distributions, you will most likely find that you have millions of these assumptions in your linear combinations, sample renormalization, regressions, sharpe weighters and optimizations. Now of course you could refine that with students, lognormals, and whatever, but this is more _refinement_ than anything.
  - g15jv2dp 2y ago
    Please quote a Nobel prize (well, there's no Nobel prize in economy, but surely we understand each other) winner explaining that stock prices are, in actual reality, random variables.
    - Galanwe 2y ago
      > explaining that stock prices are To be pedantic, stock returns, not prices. As for the quotes, I encourage you to strongly think about the meaning of the work of Sharpe, Black & Scholes and Markowitz applied to non normal distributions (both Nobel prizes, we understand each other). In particular, try to articulate the relevancy of sharpe ratios between two non normally distributed portfolios.
      - g15jv2dp 2y ago
        > To be pedantic, stock returns, not prices. If one is a random variable, so is the other. It's a simple change of variables. What's your point? > As for the quotes, I encourage you to strongly think about the meaning of the work of Sharpe, Black & Scholes and Markowitz applied to non normal distributions (both Nobel prizes, we understand each other). Could you quote the part where they say that actual, real-world stock prices (or returns, whatever) are random?
        Galanwe 2y ago
        > If one is a random variable, so is the other. It's a simple change of variables. What's your point? Not sure I follow your reasoning. Prices are positive only, and non stationary. That is very much not the same for returns. Usually prices are log normal, leading to normal (log) returns. > Could you quote the part where they say that actual, real-world stock prices (or returns, whatever) are random? It is not said, but rather implied. Take the Sharpe ratio for instance, it is a measure that: 1) is used to compare different assets / portfolio returns 2) rely on the 2nd moment of the returns. The standard deviation is less relevant the further away from the normal distribution you go, so since this is a comparison metric, it can only be reasonably applied to compare normally distributed returns. If you believe the returns are not generally normal, then you reject the use of the Sharpe ratio as a relevant measure of comparison. I don't have a B&S reference at hand, and I did not read it since 15 years, but I'm pretty sure it assumes lognormals prices as well.
lotsofpulp 2y ago
>On the contrary, these risk adjusted measures assume nothing more than a normally distributed random variable. That is exactly what I am referring to. For example, from Wikipedia: https://en.wikipedia.org/wiki/Sharpe_ratio https://en.wikipedia.org/wiki/Sharpe_ratio >However, financial assets are often not normally distributed, so that standard deviation does not capture all aspects of risk. Ponzi schemes, for example, will have a high empirical Sharpe ratio until they fail. Similarly, a fund that sells low-strike put options will have a high empirical Sharpe ratio until one of those puts is exercised, creating a large loss. In both cases, the empirical standard deviation before failure gives no real indication of the size of the risk being run. >Do you have any sort of reasoning or is it just a gut feeling? The reasoning is that their volatility is negligible over the long term due to political forces. Of course, it is also an assumption that could be wrong, but the mechanisms for government policy (democracy, aging demographics, and voter participation trends) seem to favor reducing purchasing power of currency rather than letting broad market equity prices stall or slide down.
- Galanwe 2y ago
  > >However, financial assets are often not normally distributed, so that standard deviation does not capture all aspects of risk Volatility not being a full measure of risk obviously does not imply that volatility should be ignored. The former statement about returns not being normally distributed is a, trivially verifiable, factual mistake. Daily stock returns are normally distributed with a slight positive kurtosis. This remains true on any period over the last 30 years. I am bot arguing either that the Sharpe is an all encompassing measure, some strategies have a returns distribution that is not well explained by Sharpe. I don't think it matters in this argument though.
bumby 2y ago
>assume nothing more than a normally distributed random variable But look at something like systemic risk: it’s not necessarily normally distributed. The S&P returns skew left. I’m sure there are other risk metrics that break this assumption as well.
- Galanwe 2y ago
  Right, risk is often fat tailed, but unless we enter an expert discussion, for which HN is hardly a good medium, it is safe to assume 99% of strategies out there yield normally distributed returns. Non normally returned strategies are rarer and sophisticated.
  - bumby 2y ago
    >it is safe to assume 99% of strategies out there yield normally distributed returns. I don’t know that I agree. If the market as a whole doesn’t have normally distributed risk, it implies even the simplest strategy of buying SPY and holding will also not have normally distributed risk.
  - Maxatar 2y ago
    The level of discussion that HN is a good medium for has absolutely no bearing or causal relationship with whether or not the actual stock market is normally distributed. Imagine really thinking that the nature of a discussion forum can somehow influence the distribution of stock prices, as if stock prices examine comments on the Internet to determine their behavior.
    - kjellsbells 2y ago
      I dont have a dog in this hunt but that seems like a strangely aggressive response. Perhaps the comment meant nothing more than that plaintext HN is a difficult place to start having a discussion that really requires some mathematical machinery, and therefore, since we cant throw around sigmas and integral signs here, we will make some assumptions. Attacking the comment with sarcasm isn't in the spirit of HN even if you think that is a dumb idea.

g15jv2dp 2y ago

> On the contrary, these risk adjusted measures assume nothing more than a normally distributed random variable. The financial sector isn't yet so unrelated to reality that the price of securities is random.

Galanwe 2y ago
I think when stating your opinion against 40 years of econometrical research, including multiple Nobel prizes in economy, you should feel enticed to explain your opinion a bit more than "no I don't think so"...
- Maxatar 2y ago
  This is absolutely absurd. Economists including Nobel prize winners, including even Eugene Fama who proposed the Efficient Market Hypothesis, does not think the stock market is normally distributed. At best, using a normal distribution is something that undergrads use as a tool to learn about the stock market and make some simplifying assumptions for pedagogical purposes, but it most certainly is not something that actual professionals or researchers in the field genuinely believe.
  - Galanwe 2y ago
    Come on, don't create a trial of nitpicking. I am not saying returns are a law of nature meant to teach us normality. My point is that, for all intent and purposes, you should assume normal distribution of returns. If you don't, you're obviously on either end of the spectrum: not knowing the subject at all, or nitpicking expertise on the internet. The subject of the matter here is convincing someone that risk adjusted measures should be considered when comparing portfolios. This is the basic underlying modelisation that 99.99% of the finance world makes, "compare sharpes", "compare volatility adjusted returns". I'm stating 1+1=2 and you're arguing it doesn't hold in Z/2. > At best, using a normal distribution is something that undergrads use as a tool to learn about the stock market and make some simplifying assumptions for pedagogical purposes Implicit normality assumptions are everywhere. I encourage you to think hardly about your model and question whether anything you do would work on non normal distributions, you will most likely find that you have millions of these assumptions in your linear combinations, sample renormalization, regressions, sharpe weighters and optimizations. Now of course you could refine that with students, lognormals, and whatever, but this is more _refinement_ than anything.
- g15jv2dp 2y ago
  Please quote a Nobel prize (well, there's no Nobel prize in economy, but surely we understand each other) winner explaining that stock prices are, in actual reality, random variables.
  - Galanwe 2y ago
    > explaining that stock prices are To be pedantic, stock returns, not prices. As for the quotes, I encourage you to strongly think about the meaning of the work of Sharpe, Black & Scholes and Markowitz applied to non normal distributions (both Nobel prizes, we understand each other). In particular, try to articulate the relevancy of sharpe ratios between two non normally distributed portfolios.
    - g15jv2dp 2y ago
      > To be pedantic, stock returns, not prices. If one is a random variable, so is the other. It's a simple change of variables. What's your point? > As for the quotes, I encourage you to strongly think about the meaning of the work of Sharpe, Black & Scholes and Markowitz applied to non normal distributions (both Nobel prizes, we understand each other). Could you quote the part where they say that actual, real-world stock prices (or returns, whatever) are random?
      - Galanwe 2y ago
        > If one is a random variable, so is the other. It's a simple change of variables. What's your point? Not sure I follow your reasoning. Prices are positive only, and non stationary. That is very much not the same for returns. Usually prices are log normal, leading to normal (log) returns. > Could you quote the part where they say that actual, real-world stock prices (or returns, whatever) are random? It is not said, but rather implied. Take the Sharpe ratio for instance, it is a measure that: 1) is used to compare different assets / portfolio returns 2) rely on the 2nd moment of the returns. The standard deviation is less relevant the further away from the normal distribution you go, so since this is a comparison metric, it can only be reasonably applied to compare normally distributed returns. If you believe the returns are not generally normal, then you reject the use of the Sharpe ratio as a relevant measure of comparison. I don't have a B&S reference at hand, and I did not read it since 15 years, but I'm pretty sure it assumes lognormals prices as well.

lotsofpulp 2y ago

>On the contrary, these risk adjusted measures assume nothing more than a normally distributed random variable. That is exactly what I am referring to. For example, from Wikipedia: https://en.wikipedia.org/wiki/Sharpe_ratio https://en.wikipedia.org/wiki/Sharpe_ratio >However, financial assets are often not normally distributed, so that standard deviation does not capture all aspects of risk. Ponzi schemes, for example, will have a high empirical Sharpe ratio until they fail. Similarly, a fund that sells low-strike put options will have a high empirical Sharpe ratio until one of those puts is exercised, creating a large loss. In both cases, the empirical standard deviation before failure gives no real indication of the size of the risk being run. >Do you have any sort of reasoning or is it just a gut feeling? The reasoning is that their volatility is negligible over the long term due to political forces. Of course, it is also an assumption that could be wrong, but the mechanisms for government policy (democracy, aging demographics, and voter participation trends) seem to favor reducing purchasing power of currency rather than letting broad market equity prices stall or slide down.

Galanwe 2y ago
> >However, financial assets are often not normally distributed, so that standard deviation does not capture all aspects of risk Volatility not being a full measure of risk obviously does not imply that volatility should be ignored. The former statement about returns not being normally distributed is a, trivially verifiable, factual mistake. Daily stock returns are normally distributed with a slight positive kurtosis. This remains true on any period over the last 30 years. I am bot arguing either that the Sharpe is an all encompassing measure, some strategies have a returns distribution that is not well explained by Sharpe. I don't think it matters in this argument though.

bumby 2y ago

>assume nothing more than a normally distributed random variable But look at something like systemic risk: it’s not necessarily normally distributed. The S&P returns skew left. I’m sure there are other risk metrics that break this assumption as well.

Galanwe 2y ago
Right, risk is often fat tailed, but unless we enter an expert discussion, for which HN is hardly a good medium, it is safe to assume 99% of strategies out there yield normally distributed returns. Non normally returned strategies are rarer and sophisticated.
- bumby 2y ago
  >it is safe to assume 99% of strategies out there yield normally distributed returns. I don’t know that I agree. If the market as a whole doesn’t have normally distributed risk, it implies even the simplest strategy of buying SPY and holding will also not have normally distributed risk.
- Maxatar 2y ago
  The level of discussion that HN is a good medium for has absolutely no bearing or causal relationship with whether or not the actual stock market is normally distributed. Imagine really thinking that the nature of a discussion forum can somehow influence the distribution of stock prices, as if stock prices examine comments on the Internet to determine their behavior.
  - kjellsbells 2y ago
    I dont have a dog in this hunt but that seems like a strangely aggressive response. Perhaps the comment meant nothing more than that plaintext HN is a difficult place to start having a discussion that really requires some mathematical machinery, and therefore, since we cant throw around sigmas and integral signs here, we will make some assumptions. Attacking the comment with sarcasm isn't in the spirit of HN even if you think that is a dumb idea.