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When might you want the mean?

Examples from finance:

  • Bond returns:
    • The median bond return will generally be a few percentage points.
    • The mean bond return might be low or high depending on the default rate and recovery in default. The median will ignore all this!
    • Good luck explaining to your investors, "I know our fund is down 40% this year because almost half are bonds went bust with no recovery, but our median bond returned 1%!"
  • Venture capital returns:
    • Same thing in reverse. The median VC or angel investment is a bust, and all the return comes from a few winners! (Side note/warning: estimates of venture capital or private equity returns are highly problematic... be careful!)

When forming a diversified portfolio, deciding what to invest in and how much, the mean and covariance of returns are likely to factor prominently into your optimization problem.

When might you want the mean?

Examples from finance:

  • Bond returns:
    • The median bond return will generally be a few percentage points.
    • The mean bond return might be low or high depending on the default rate and recovery in default. The median will ignore all this!
    • Good luck explaining to your investors, "I know our fund is down 40% this year because almost half are bonds went bust with no recovery, but our median bond returned 1%!"
  • Venture capital returns:
    • Same thing in reverse. The median VC or angel investment is a bust, and all the return comes from a few winners!

When might you want the mean?

Examples from finance:

  • Bond returns:
    • The median bond return will generally be a few percentage points.
    • The mean bond return might be low or high depending on the default rate and recovery in default. The median will ignore all this!
    • Good luck explaining to your investors, "I know our fund is down 40% this year because almost half are bonds went bust with no recovery, but our median bond returned 1%!"
  • Venture capital returns:
    • Same thing in reverse. The median VC or angel investment is a bust, and all the return comes from a few winners! (Side note/warning: estimates of venture capital or private equity returns are highly problematic... be careful!)

When forming a diversified portfolio, deciding what to invest in and how much, the mean and covariance of returns are likely to factor prominently into your optimization problem.

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source | link

When might you want the mean?

Examples from finance:

  • Bond returns:
    • The median bond return will generally be a few percentage points.
    • The mean bond return might be low or high depending on the default rate and recovery in default. The median will ignore all this!
    • Good luck explaining to your investors, "I know our fund is down 40% this year because almost half are bonds went bust with no recovery, but our median bond returned 1%!"
  • Venture capital returns:
    • Same thing in reverse. The median VC or angel investment is a bust, and all the return comes from a few winners!