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A monkey throwing darts will outperform the market on average. The monkey is giving even weight to each option rather than weighting according to risk. The mon

A monkey throwing darts will outperform the market on average. The monkey is giving even weight to each option rather than weighting according to risk. The monkey is picking a riskier portfolio than an index fund, and in compensation for accepting greater downside risk will have greater average returns. Markets are subtle like that =) Of course, the monkey is likely to attribute the difference to skill rather than risk...

lisper 9y ago
That assumes that risk is not symmetrically distributed. That might be the case, but that would be news to me.
- jjoonathan 9y ago
  Why would it be symmetrically distributed?
  - lisper 9y ago
    Good question. It actually doesn't have to be symmetric, it just has to be distributed in such a way that a random sample will not give you a biased return. (A symmetric distribution is sufficient but not necessary.) The reason this has to be the case is that if a random portfolio gave you a biased return, then the sum of random portfolios would give you a biased return. But the limit of the sum of random portfolios is the whole market, and that can't be biased.
    - jjoonathan 9y ago
      Perhaps it's easier to see from the other side: the monkey is getting the same expected returns as "buy one of everything on your list," but the index fund is not, because the index fund is employing a different weighting strategy (e.g. buy the 30 or 500 largest companies). Of course, if you define "market" using the same list that an index fund uses, the monkey's expected performance converges with that of the index fund.
      - icebraining 9y ago
        That depends on the fund, some track indexes like the CRSP U.S. Total Market, which has almost 100% of the US equity market.
fitchjo 9y ago
Not sure I follow your logic: 1. What are you calling the market in your first sentence? 2. Why/how is an index fund somehow less risky? What is the fund indexing and how does that compare to the market in your first sentence? In your scenario, if the index fund is properly designed to capture the risk of the "market" as you have defined it, a monkey has equal chance of performing better or worse than the index fund and the average monkey (or an average of a large enough set of monkeys) will perform with the index fund. Certainly, though, if your index fund is not designed to be reflective of the market, but of some subset, then it will carry different risk, but not necessarily less risk. However, a monkey randomly picking stocks from a pool will not, on average, outperform the average return of that pool of stocks.
- jjoonathan 9y ago
  An index fund is more likely to invest in BoringBigCo than NewShinyCo. The monkey is equally likely to invest in BoringBigCo and NewShinyCo. The latter strategy has more risk.

lisper 9y ago

That assumes that risk is not symmetrically distributed. That might be the case, but that would be news to me.

jjoonathan 9y ago
Why would it be symmetrically distributed?
- lisper 9y ago
  Good question. It actually doesn't have to be symmetric, it just has to be distributed in such a way that a random sample will not give you a biased return. (A symmetric distribution is sufficient but not necessary.) The reason this has to be the case is that if a random portfolio gave you a biased return, then the sum of random portfolios would give you a biased return. But the limit of the sum of random portfolios is the whole market, and that can't be biased.
  - jjoonathan 9y ago
    Perhaps it's easier to see from the other side: the monkey is getting the same expected returns as "buy one of everything on your list," but the index fund is not, because the index fund is employing a different weighting strategy (e.g. buy the 30 or 500 largest companies). Of course, if you define "market" using the same list that an index fund uses, the monkey's expected performance converges with that of the index fund.
    - icebraining 9y ago
      That depends on the fund, some track indexes like the CRSP U.S. Total Market, which has almost 100% of the US equity market.

fitchjo 9y ago

Not sure I follow your logic: 1. What are you calling the market in your first sentence? 2. Why/how is an index fund somehow less risky? What is the fund indexing and how does that compare to the market in your first sentence? In your scenario, if the index fund is properly designed to capture the risk of the "market" as you have defined it, a monkey has equal chance of performing better or worse than the index fund and the average monkey (or an average of a large enough set of monkeys) will perform with the index fund. Certainly, though, if your index fund is not designed to be reflective of the market, but of some subset, then it will carry different risk, but not necessarily less risk. However, a monkey randomly picking stocks from a pool will not, on average, outperform the average return of that pool of stocks.

jjoonathan 9y ago
An index fund is more likely to invest in BoringBigCo than NewShinyCo. The monkey is equally likely to invest in BoringBigCo and NewShinyCo. The latter strategy has more risk.