Economic Value of Prediction of Return Distribution

Abstract

Modeling the distribution of asset returns is crucial in constructing financial portfolios. Accurate and timely modeling of the distribution of asset returns paves the way for the construction of portfolios using these distributions that can provide higher return/volatility performance compared to conventional assets such as the market index. This paper proposes a modeling approach by considering the relationship between the average and volatility of returns of S&P 500 over the period of 2000-2019. The joint distribution of the returns and their volatility is modeled by explicitly incorporating the links between the returns and volatility. This is executed by allowing for asymmetric relations between the mean and volatility. Capturing the timing and asymmetrical nature of these relationships provides a much better estimation of the asset distribution and its volatility. Predictions of real-time return distributions are formed based on this model. The model’s performance is evaluated from the point of a representative investor constructing her portfolio using real-time forecasts based on this model. This investor determines the portfolio weights based on the outcome of the econometric model explicitly capturing the relationship between expected return and volatility in each period. Results show that the link between returns and their volatility bears considerable economic value. Moreover, the findings remain robust to various effects.

Keywords

• Volatility
• Expected Return
• Return Distribution

Getiri Dağılımı Tahmininin Ekonomik Değeri

Abstract

Varlık getirilerinin istatistiki dağılımını modellemek özellikle finansal portföylerin oluşturulmasında çok önemlidir. Varlık getirilerinin dağılımının doğru ve zamanlı modellenmesi, bu dağılımlar yardımıyla oluşturulan portföylerin de piyasa endeksi gibi geleneksel finansal varlıklara göre daha yüksek getiri/oynaklık performansı sağlamasının önünü açacaktır. Bu makalede, 2000-2019 döneminde S&P 500 Endeks getirilerinin ortalaması ve oynaklığı arasındaki kaldıraç ilişkisi de ele alınarak bir modelleme yoluna gidilmiştir. Bu yapılırken de özellikle beklenen getiri ve oynaklık arasındaki asimetrik ilişki dikkate alınmıştır. Bu ilişkilerin hem zamanlamasının hem de asimetrik yapısının uygun bir şekilde ele alınması varlık dağılımının ve bu dağılımın volatilitesinin çok daha iyi tahmin edilmesini sağlamaktadır. Modelin başarısı, bu modelden yola çıkarak oluşturulan gerçek zamanlı tahminleri kullanarak yatırım yapan bir temsili yatırımcı gözüyle değerlendirilmiştir. Bu yatırımcı her zaman periyodunda beklenen getiri oynaklık arasındaki ilişkiyi bütünüyle ele alan ekonometrik model yardımıyla portföy ağırlıklarını belirlemektedir. Bu ağırlıklar sonucunda gerçekleşen portföy getirisinin temsili yatırımcıda yarattığı ortalama fayda modellerin başarı ölçütü olarak kullanılmıştır. Sonuçlar beklenen değer ve oynaklık arasındaki ilişkinin ekonomik değerinin oldukça yüksek olduğunu göstermiştir. Bu sonuçlar birçok farklı etmene karşı geçerliliğini korumaktadır. Dolayısıyla finansal portföy oluşumunda sadece getiri ve oynaklık değil, bu ikisi arasındaki ilişkinin de modellenmesi önerilmektedir.

Keywords

• Oynaklık
• Beklenen Getiri
• Getiri Dağılımı

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