The Short-Term and Long-Term Trade-Off Between Risk and Return: Chaos vs Rationality

Abstract

This paper used the composite construction method proposed by Haugen (1999) and its application by Zhao and Wang (2010) for the Chinese stock market. Utilizing the Shanghai A-share market stocks data, this paper first selected the shares listed on the Shanghai Stock Exchange during January 1, 1997 to December 31, 2017. A portfolio was then built according to the mean variance model of portfolio structure, and simulation results were analysed using the Wilcoxon Signed Rank Test. The relationship between risk and return in the long and short term was explored. Results indicated no significant relationship between the risk and return of the stock portfolio in the short run, which reflects the complexity of the Chinese stock market. However, in the long run, the risk and return of the stock portfolios are positively correlated, which means that high returns are accompanied by high risks, indicating that the stock market will eventually return to rationality. In other words, the A-share stock market will eventually return to be value-driven and the short-term speculators would be outweighed by long-term value investors.

The Probabilistic Risk Measure VaR as Constraint in Portfolio Optimization Problem

“…The main assumption applied for the forecast of the assets characteristics is the precise identification now and assuming same level of the asset characteristics in the future [4]. That is why the precise identification now has been under the scope and development of several identification procedures [10]. Here we are going to mention the ARMA and GARCH approaches for the estimation of the assets returns.…”

“…The initial probabilistic inequality comes from the definition of the cumulative distribution function F(.) of a stochastic variable X and its expression with the probability of the probability density function P(X) or (10) 𝐹(𝑥) = 𝑃(𝐗 < 𝑥) ≥ 𝛼 or 1 − 𝐹(𝑥) = 𝑃(𝐗 > 𝑥) ≤ 𝛼, where x is a value of the stochastic variable X, α is a value of the probability P.…”

“…Hence from (7) it follows (11) VaR 𝛼 = min{𝛾 ∶ 𝑃(𝐘 > 𝛾) ≤ 1 − 𝛼} . Relation (11) can be expressed in form (10) as (12) 𝑃(𝐘 < 𝛾) ≥ 𝛼, because Y has meaning of portfolio losses, which is expressed as negative portfolio return relation ( 12) becomes ( 13) 𝑃(𝐘 < −𝛾, (−1)) ≥ 𝛼 = 𝑃(−𝐘 > −𝛾) ≥ 𝛼, where the negative Y has new meaning as portfolio return and according to its definition it follows -Y=𝐑 T 𝐰 and ( 13) is rewritten as (14) 𝑃(𝐑 T 𝐰 > −𝛾) ≥ 𝛼, where γ=VaRα. To include the probabilistic inequality (14) in the portfolio problem (5) it is needed all parameters of ( 14) to be expressed with portfolio arguments w and parameters 𝚺 and E. Respectively, ( 14) from probabilistic it must be presented as analytical constraint.…”

“…Considering the equivalent relation(10) which gives 1 − 𝐹(𝑥) = 𝑃(𝐗 > 𝑥), −1 [(1 − 𝛼)], or (16) 𝐄 T 𝐰 + 𝐹 −1 [(1 − 𝛼)]√𝐰 T 𝚺𝐰 ≥ −𝛾. The value 𝐹 −1 [(1 − 𝛼)] is taken from the z-score tables about the inverse cumulative function for stochastic process with zero mean and standard deviation equals 1 [23].…”

Exploring the trade-off between liquidity, risk and return under sectoral diversification across distinct economic settings

“…Besides, the relationship between risk and return is not straightforward. For example, Liu et al (2020) were able to ascertain that no significant relationship between risk and return exists in the portfolios of stocks of the Chinese stock market in the short run. Nevertheless, they were able to establish that the risk and return of the portfolios of stocks were positively correlated in the long run.…”