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Portfolio construction

Fractional Kelly

A fixed share of the Kelly portfolio, half by default: most of the growth with much smaller swings.

2 دقیقه مطالعه · در بهینه‌ساز سبد امتحان کنید ↗

ایده به زبان ساده

The growth curve is flat near its top: betting half of Kelly still earns three quarters of the maximum growth, with half the volatility and far shallower drawdowns. And because Kelly overbets when the estimates are too rosy, a fraction is also insurance against your own errors.

روش محاسبه

Compute the Kelly weights, multiply by the fraction (Settings › Kelly fraction, 0.5 by default), then apply the maximum-leverage cap.

w = c × w_Kelly,   0 < c ≤ 1
g(c) = c(2 − c) × g_max     (½ Kelly → 75% of the growth, 50% of the volatility)

نحوه استفاده

  • The practical way to use Kelly: start at 0.25–0.5.
  • Lower the fraction when you trust the estimates less (short history, few tickers).

نتیجه‌گیری

  • If Fractional and full Kelly give the same weights, both hit the leverage cap.
  • The growth column in the study shows what the fraction gives up.

مثال

Running example (used in every portfolio guide): US500, GER40, gold (XAUUSD) and EURUSD, two years of daily data. Expected returns 8%, 7%, 7% and 1% a year; volatilities 18%, 20%, 15% and 7%. US500 and GER40 move together (correlation about 0.7); gold hardly moves with the indices (about 0.04). Half of the full Kelly portfolio would still be 2.7× leverage, so here it also hits the 2× cap and comes out the same as full Kelly (80% US500, 10% GER40, 111% gold). Lower the maximum leverage or the fraction (0.25 gives 1.35×) to see it differ.

ورودی‌های مثال نمایشی‌اند؛ وزن‌ها و ارقام همان چیزی است که بهینه‌ساز ما برایشان برمی‌گرداند.

مراقب این‌ها باشید

  • Still leveraged in many cases; check the gross exposure.
  • The fraction does not fix wrong estimates; it only limits the damage.

کمی تاریخچه

Fractional Kelly was studied by MacLean, Thorp and Ziemba among others; Thorp and many professional gamblers and investors have long recommended half Kelly or less.

فقط محتوای آموزشی. هیچ مدل سبدی آینده را نمی‌داند: همه با برآوردهایی از گذشته کار می‌کنند و هیچ‌چیز اینجا توصیه سرمایه‌گذاری نیست.