勝率と成績の安定性

前の記事で「勝率が高いほど適切なリスクは高くできる」と書きました。

「取るリスクは2%以下にすべし」は本当か?

いったいなぜなのか疑問に感じた思います。
今回はこの理由について掘り下げて考察していこうと思います。

勝率が高いと資産の変動幅が少なくなる(安定する)勝率が低いと資産の変動幅が大きくなる(ばらつく)

勝率が高く損益率が低いと、トレードを重ねても資産がある程度の狭い範囲にまとまる傾向があります。
逆に勝率が低く損益率が高いと、トレードを重ねるにつれ資産が広い範囲にばらつく傾向があります。
期待値0の条件で、勝率や損益率を変えてリスク1%固定で100回のトレード×1000回の試行をした結果、資産がいくらになったのかをまとめたグラフです。

1000回の試行の結果の標準偏差をグラフにすると次のようになります。

勝率が低くなるにつれ急速に標準偏差(ばらつき)が大きくなっているのがわかります。
もちろんどのトレードも期待値は0なので、100回のトレード結果の平均をとるとどれも初期資産100万円とほぼ変わりません。
勝率が高いほど、100回トレードをした後の資産が100万円付近に集中しています。
逆に勝率が低いほど、資産が広い範囲にばらついています。
つまり、
勝率が高い方が安定性が高くなる
勝率が低い方がばらつきが大きくなる
ということです。

いったいなぜ勝率が高いと安定するのか?

なぜ勝率が高いと安定するのでしょうか?
これは単純に平均的な資産の変化幅が小さいからと解釈できます。
例えば
高勝率トレード・・・勝率90% 損益率0.111 期待値0 損切100pips 利確11.1pips
低勝率トレード・・・勝率10% 損益率9 期待値0  損切100pips 利確900pips
というトレードをしたとします。どちらもロット数とリスクは同じとします。

高勝率トレードにおいて期待される損益は
勝ちトレード・・・90%×11.1pips = 9.99
敗けトレード・・・10%×-100pips = -10.0
となり結果として期待値は(ほぼ)プラスマイナス0となります。

一方低勝率トレードにおいて期待される損益は
勝ちトレード・・・10%×900pips = 90
敗けトレード・・・90%×-100pips = –90
となります。期待値はこちらもプラスマイナス0です。

これをみると、期待値が0でもその変動幅は低勝率トレードの方が大きいことがわかります。大きな変動幅を伴うトレードが繰り返される結果としてばらつきが大きくなっているということです。
高勝率トレードは結果が安定することから、大きなリスクを取っても破産リスクが高まりにくいのです。
これが高勝率トレードにおいて適切なリスクが高くなる理由です。

まとめ

期待値が同じで、リスクも同じ条件でも高勝率トレードの方が安定する
逆に低勝率トレードは結果がばらつく
高勝率トレードは結果のばらつきが少ないので、大きなリスクを取っても破産リスクが上昇しにくい ⇒ 高勝率トレードにおいて適切なリスクが大きくなる理由

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  1. […] これまでの記事で、勝率が高いと資産が安定して増えていく勝率と成績の安定性適切なリスクは、勝率が高いほど高くなる=勝率が高いトレードであれば大きなリスクをとれる期待値と […]

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