Introduction

The fund management is a tricky situation of managing the stock investment. The implication of fund management is to ensure that the investor or fund manager obtains the highest return and minimal risks using the appropriate asset allocation strategy. The basis of investment is to provide a highest return that will make the fund manager able to attain the investment goals. In this case, the fund manager will have two stocks to manage the £1m fund comprising 2 assets comprising of cash and FTSE equity (BP stock). In this case the allocation fund needs to be used to maximize the fund return for the month and make a balance to ensure the weekly volatility of the fund does not exceed 2.0%. the critical aspect requires the volatility model and its parameters by Modelling the equity’s volatility. The model will be allocating and asset to maximize the fund monthly return within the fund volatility constraint and predict the return and volatility. In this case one will use the investment, monitor the price and equity action as well as the actual returns and volatility for each of the 4 weeks and compare the actuals against your predictions.

Summary of Volatility

The cash volatility for the cash fund is estimated to 2.23% over the next 4 weeks whereas BP stock volatility is estimated to be 3.38%. Due to the uncertainty in the market BP stock has a higher volatility rate because of the fact that there is a fluctuation in the stock market. On the other hand, the cash fund has a relatively lower volatility because it may slightly be affected by the change in the macroeconomic forces in the market such as inflation and other adverse issues (Hung., Lien, & Chien,2020).

The change in the timelines may change the fund manager risk or volatility in the stock selection for the fund because multiple changes in the timelines because short term perspective of investment may change because some stocks or fund will perform better in the long run whereas others may perform better in the short run (Stafylas, Andrikopoulos & Tolikas, 2023).In this case, the cash fund performs better in the first four weeks because it has a zero-stock return and also has a relatively lower average volatility which is 2.23%. However, the BP stock fund performance is relatively lower with a -1.232% but has a relatively attain a loss. This means that BP stock performance may not be known because of the variation in the stock market because it is not static. Therefore, it is expected the performance may change based on the changes in the market and variation in the stock performance(Stafylas, Andrikopoulos & Tolikas, 2023)

The funds invested will be available in the market hence understanding the volatility which will lead to the investment outcome based on the fund managers risk profile and investment objectives. The potential volatility of the fund will allow the investor align towards expectation of the actual performance of the investment (Hung., Lien, & Chien,2020). The fund manager will need to assess the risk-reward parameters in the investment and select the appropriate fund which will fit the risk profile. However, the fund volatility factor will guide the fund manager to assess the potential volatility of returns based on the returns in the past. Thus, the volatility will assess how the returns will fluctuate which will enable the fund manager asses whether the stock is suited to the risk tolerance

. The equity fund will have Fund volatility factor which will range from the low to very high which means that the small cap stock which is volatile and dividend yield stocks. The equity funds require the focus on investment and have a higher volatility compared to cash. The investor has an aggressive risk tolerance may select the funds with high and very high fund value component. Hence, the funds may deliver the returns but will attain the higher levels of volatility in the returns. The fund volatility factor will involve the risk classification which will offer the fund manager the information on the risk profile to make good investment decisions. In the selection of the appropriate fund categories, the fund manager will have to assess the potential fund risks measured by FVF and FVC indicators and remain focused on the long-term investment objectives and risk profiles.

Fig 2:   Cash and BP stock returns & Volatility

Volatility model design and realization

Autoregressive conditional heterodaskacity (ARCH)

According to Song, & Jing, (2022) the volatility of the stock fund is determined using the time-varying model known as the autoregressive conditional heterodaskacity (ARCH) which is first determined using the mean and variance as the first and second moment. The ARCH is a deterministic function of the historical return which is expressed and hence an observable variable. Hence, the discrete time stochastic model with two set of measurement equation which is based on the observed returns and realized measure is linked to the latent conditional variables (Song, & Jing, 2022).This means that an effective variant will provide an algorithm for effective filtering and smooth realized measure in latent volatility persistent. This model may be extended to arrive at the generalized autoregressive conditional heterodaskacity (GARCH) which is a deterministic function of the distributed lag of the past squared observations (Schäfers, & Teng, 2022). Thus, the GARCH will capture the capture the excess returns of the financial times which is linked to the performance restriction. The model assert that the stock volatility is negatively correlated to the price movement because of increased leverage which eventually increased the volatility. However, the Stochastic Volatility Model (SVM) act contrary to the GARCH model because the past stock return. The stock price will move through a sequence of equilibrium, which compels one to move from one equilibrium point to another due to the existence of new information or news in the market which might change the price movement of the distinct stock in the market (Song, & Jing, 2022). This may also be attributed to the agent action which will compel it to model the information based as a latent variable (Schäfers, & Teng, 2022). The model explains that the changes in the stock is not a coincident but attributed to the changes in the market such as news and regular update due to the uncertainty and market forces that exist in the market. As a result, the volatility and price movement may pool in various direction depending on the existing situation in the market and the time. In the evaluation of the funds, the model. However, the model is criticized because of having varying variance (Schäfers, & Teng, 2022).

Stochastic Volatility Model (SVM)

The model is a stochastic concept used in estimating stochastic volatility. The model has an interactive function Stochastic Volatility Model (SVM) deals with the past stock return (Song, & Jing, 2022). The stock price will move through a sequence of equilibrium, which compels one to move from one equilibrium point to another due to the existence of new information or news in the market which might change the price movement of the distinct stock in the market. This may also be attributed to the agent action which will compel it to model the information based as a latent variable(Schäfers, & Teng, 2022). The assessment reveals that the posterior mean is 0.87 and 0.92 which is closer to one. This is evidence of persistence conditional variance. Due to the fact that the model is less than one, it supports the assertion that hypothesis mean will revert to volatility. This indicates that the random shocks to volatility will tapper half of the few weeks. The estimated volatility measured by the standard deviation shows that the fund BP stock and Cash are 0.15 and 0.19 respectively. The value is a good measure of fit of the volatility equation. Similarly, the volatility parameters are closer to the mean which indicates that it is statistically significant. The mode volatility of the fund also ranges from 1.49 and 1.38 which indicates that the daily news occurs frequently and have a general impact on the stock movement and performance in the market(Schäfers, & Teng, 2022). As a result, the SVM tend to capture the market performance and behavior of the stock indices fund.

Asset Allocation

The allocation of the asset depends on the market performance of the stock; since the fund manager is risk averse, then it is advisable to employ the efficient allocation which include allocating 50% of stocks comprising of BP stock and 50% on cash. the allocation is based on the fund diversification strategy to minimize the risk that may be inherent in the market. In allocating the assets, the weekly stock return on average will be compared to reflect the proportion. In the first four week, the BP stock will yield a relatively higher return compared to the cash with an estimated return of 0.31% (1552.3) but has a higher volatility due to the uncertainty in the market. However, in the 3-month or quarterly period, the assets yield a proportion of -1.232% for the equity funds stock which translate to an overall loss of £6160.62 for the BP stock and the cash fund yield a zero amount. This is because the cash available will be estimated has a fixed value which might not change with time because of the static nature of the fund. However, in the allocation of the asset, the fund manager will need to strike a balance based on the past performance because he is well acquainted with handling various stocks. In this case, the fund manager has struck a balance in allocating the asset equally. This means that the fund manager may change the stock allocation or asset allocation after seeing the first four-week performance of the stock. As a result, she may allocate more cash asset fund such as 40% BP stock (Equity Fund) and 60% cash because of the performance of the cash versus the equity fund.

Table 1: Asset Allocation (4-weeks)

Table 1: Asset Allocation (3-month)

Fig 3Table with Actual Price and Volatility (3-Month Volatility)

 Fig 4: Actual Price and Volatity 4-Weeks

Commentary on differences and modelling process

The ARCH or GARCH model indicates that the stock volatility is negatively correlated to the price movement because of increased leverage which eventually increased the volatility (Song, & Jing, 2022). However, the Stochastic Volatility Model (SVM) act contrary to the GARCH model because the past stock return whereas the SVM deals with the current stock prices(Ma, 2022). The stock price will move through a sequence of equilibrium, which compels one to move from one equilibrium point to another due to the existence of new information or news in the market which might change the price movement of the distinct stock in the market (Song, & Jing, 2022).. Additionally, SVM have a varied number of variances which is unlike the GARCH model which the variance are fixed and depends on the existing elements or variables in the model. Additionally, the mean for the model in GARCH is relatively lower compared to the one obtained using the SVM model (Ma, 2022).

Commentary on asset suitability for a fund

As a result of the assessment, it is evident that the stock composition makes the fund more suitable to the investor because the allocation is slightly efficient(Ma, 2022). Therefore, the general fund will be able to make the fund manager obtain a suitable return on investment (Song, & Jing, 2022). This means that the fund can also be made allocative efficient by increasing more of the BP stock percentage allocation to more than 60 percent and that of cash reduced to 40% and above due to the distinct performance of each stock in the last four weeks.

Conclusion

The fund manager has to be created a balance of fund by changing the proportion of the allocation until the fund is balanced. The fund need to be increased moderately in a simulation aspect preferably after the period of investing to determine which proportion will make the fund more balanced and yield more return versus the volatility

References

Hung, P. H., Lien, D., & Chien, Y. J. (2020). Portfolio concentration and fund manager performance. Review of Financial Economics, 38(3), 423-451.

Jiang, G. J., Liang, B., & Zhang, H. (2022). Hedge fund manager skill and style-shifting. Management Science, 68(3), 2284-2307.

Jiang, G. J., Zaynutdinova, G. R., & Zhang, H. (2021). Stock-selection timing. Journal of Banking & Finance, 125, 106089.

Ma, R. (2022). Hedge Fund Strategies Performance in Bad Market Condition Analysis. Highlights in Business, Economics and Management, 2, 188-195.

Samarbakhsh, L., & Shah, M. (2022). Did the STOCK Act impact the performance, risk and flow of hedge funds?. International Journal of Managerial Finance, 18(5), 944-978.

Schäfers, T., & Teng, L. (2022). Asymmetry in stochastic volatility models with threshold and time-dependent correlation. Studies in Nonlinear Dynamics & Econometrics.

Song, S., & Jing, F. (2022). Research on Parameter Estimation and Prediction of Sports Financial Market Volatility Model. Mathematical Problems in Engineering, 2022.

Stafylas, D., Andrikopoulos, A., & Tolikas, K. (2023). Hedge fund performance persistence under different business cycles and stock market regimes. The North American Journal of Economics and Finance, 64, 101866.

Appendices