This research explores the effects of adding bitcoin to an optimal portfolio (naïve, long-only, unconstrained and semi-constrained) of by relying on mean-CVaR approach in Chinese market. Then backtesting to compare the performance of portfolios with and without bitcoin for each scenario is performed. Results show significant but weak correlations between various asset classes and bitcoin, implying a more mature financial profile of bitcoin in China compared to that in the west. Backtesting results show that the effect of adding bitcoin to optimal portfolios is not consistent over the entire out-of-sample period. The naïve and the long-only strategy improved the risk reward ratio up until the late 2013 price-crash with no significant advantages thereafter. Shorting strategies on the other hand, with or without leverage, fail to produce more efficient portfolios when bitcoin is added, and this is consistent over the entire out-of-sample period. The results also show that semi-annual rebalancing amplifies the advantages of adding bitcoin to most portfolios except for the semi-constrained portfolio, although the weights analysis show significant shifts in weights which might not represent a feasible strategy in realistic scenarios.

This research explores the effects of adding bitcoin to an optimal portfolio (naïve, long-only, unconstrained and semi-constrained) of by relying on mean-CVaR approach in Chinese market. Then backtesting to compare the performance of portfolios with and without bitcoin for each scenario is performed. Results show significant but weak correlations between various asset classes and bitcoin, implying a more mature financial profile of bitcoin in China compared to that in the west. Backtesting results show that the effect of adding bitcoin to optimal portfolios is not consistent over the entire out-of-sample period. The naïve and the long-only strategy improved the risk reward ratio up until the late 2013 price-crash with no significant advantages thereafter. Shorting strategies on the other hand, with or without leverage, fail to produce more efficient portfolios when bitcoin is added, and this is consistent over the entire out-of-sample period. The results also show that semi-annual rebalancing amplifies the advantages of adding bitcoin to most portfolios except for the semi-constrained portfolio, although the weights analysis show significant shifts in weights which might not represent a feasible strategy in realistic scenarios.

This paper analyzes international portfolio selection with exchange rate risk based on behavioural portfolio theory (BPT). We characterize the conditions under which the BPT problem with a single foreign market has an optimal solution, and show that the optimal portfolio contains the traditional mean–variance efficient portfolio without consideration of exchange rate risk, and an uncorrelated component constructed to hedge against exchange rate risk. We illustrate that the optimal portfolio must be mean–variance efficient with exchange rate risk, while the same is not true from the perspective of local investors unless certain conditions are satisfied. We further establish that international portfolio selection in the BPT with multiple foreign markets consists of two sequential decisions. Investors first select the optimal BPT portfolio in each market, overlooking covariances among markets, and then allocate funds across markets according to a specific rule to achieve mean–variance efficiency or to minimize the loss in efficiency.

Fund managers usually set aside certain amount of cash to pay for possible redemptions, and it is believed that this will affect overall fund performance. This paper examines the properties of efficient portfolios in the mean-variance framework in the presence of a cash account. We show that investors will retain part of funds in cash, as long as the required return is lower than the expected rerun on the portfolio corresponding to the point of intersection of the traditional efficient frontier and the straight line that passes through the minimum-variance portfolio and the origin in the mean-variance plane (portfolio q1 ). In addition, the efficient portfolios determined by our model are proportional to portfolio q1 , and are more efficient than traditional efficient portfolios. Using a simulation, we illustrate that 6% to 9% of total funds are to be retained in the cash account if no-short-selling constraint is imposed. Based on real data, our out-of-sample empirical results confirm the theoretical findings.

This paper investigates the impact of background risk on an investor’s portfolio choice in a mean–variance framework, and analyzes the properties of efficient portfolios as well as the investor’s hedging behavior in the presence of background risk. Our model implies that the efficient portfolio with background risk can be separated into two independent components: the traditional mean–variance efficient portfolio and a self-financing component constructed to hedge against background risk. Our analysis also shows that the presence of background risk shifts the efficient frontier of financial assets to the right with no changes in its shape. Moreover, both the composition of the hedge portfolio and the location of the efficient frontier are greatly affected by a number of background risk factors, including the proportion of background assets in total wealth and the correlation between background risk and financial risk.

Efficient portfolio is a portfolio that yields maximum expected return given a level of risk or has minimum level of risk given a level of expected return.However,the optimal portfolios seem not being as efficient as intended.Especially during financial crisis period.optimal portfolio is not an optimal investment as it does not yield maximum return given a specific level of risk,vice and versa.One possible explanion for an unimpressive performance of the seemingly efficient portfolio is incorrectness in parameter estimates called"estimation risk in parameter estimates".Five different estimating strategies are employed to explore ex post portfolio performance when estimation risk is incorporated.These strategies are traditional mean-variance(EV),Adjusted Beta(AB) approach,Capital Asset Pricing Model(CAPM),Single Index Model(SIM), and Single Index Model incorporating shrikage Bayesian factor namely Bayesian Single Index Model(BSIM).Among the five alternative strategies,shrinkage estimators incorporating the single index model outperforms other traditional portfolio selection strategies.Allowing for asset mispricing and applying Bayesian shrinkage adjusted factor to each asset's alpha,a single factor namely excess market return is adequate in alleviating estimation uncertainty. JEL：G320