Investments & Risk Management
Table of Contents

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1.1 Passive Portfolio
1.1.1 Introduction
The purpose of this section is to show the passive portfolio management created five years ago for a
client who requested me to make an investment with £1,000,000. The client has specified its
investment objectives and risk appetite, it has been decided that for the first five years, the money
will be invested passively starting on January 1, 2017 and invested only in stocks/equity.
1.1.2 Investment Philosophy
According to William Sharpe’s Investment theory indicate when costs are taken into account, the
return on the average actively managed dollar can equal the return on the average passively
managed dollar, but when costs are removed, the average dollar managed actively will yield a
smaller return than the average dollar managed passively (Sharpe, 1991). The most effective
passive investment strategy is to use the buy and hold strategy, which produces better returns
than other actively managed investment funds because it keeps costs low (Sharpe, 1991). In this
context, passive portfolios were constructed using top-down approaches that gives a more
complete picture of the global economy, since it considers many variables such as GDP,
inflation, employment rates to avoid risks (Baumohl, 2010). Moreover, passive portfolio helps to
reduce risk and increase returns by considering a variety of industries and sectors (Kristjanpoller
& Olson, 2015).
1.1.3 Investor Profile
Based on macroeconomic indicators, Poland ranked in 23rd place among the 25 highest GDPs in
2021 among advanced economies. In terms of interest rate, data exported from Bloomberg shows
that Poland has a stable interest rate of 1.50% during 2015-2019 and slightly decreased in 2020
by 1.4% and became 0.10%.
The client is medium risk tolerance, which means he is willing to accept a moderate level of risk
with a moderate investment return as per the 3 questionnaires done (Bright Start, Vanguard on
AA & Standard Life). Ranjith (2002) suggests that such investors need a well-managed return in
order to stay in the market. Keeping an eye on the investor’s profile helps you understand how
you will achieve the client’s goals over the long-run. The client has selected eight sectors to
invest in.
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1.1.4 Assets Allocation
In the investment world, asset allocation is basically about balancing risk and reward by
choosing an appropriate portfolio asset based on a person’s goals, tolerance of risk, and
investment timeframe (Meucci, 2009), (Zakamulin, 2016). Investing in stocks with low P/E ratio
is the preferred criteria of the client. According to Basu (1983), stocks with low P/E ratio
outperform those with a high one. In addition, Statman (1987) states that in order to have a welldiversified portfolio, one should have at least 30 stocks in which to invest. In the passive
portfolio, the client invested in equity stocks and selected 45 companies in Poland from a variety
of sectors and industries (Oil & Gas, Healthcare, Technology, and Real Estate) with P/E ratio of
less than 12, by using the top-down approach as it is more applicable than bottom-up approach.
1.1.5 Passive Portfolio Results
The portfolio was started with an investment of £1,000,000 and after an investment period of 5
years with a passive investment strategy did very well. A total gain of £2,222,780. This money
was then reinvested into the active portfolio.
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1.2 Active Investment Portfolio
1.2.1 Introduction
The client has agreed to change the investment strategy after five years of passive investment,
and to invest actively for ten weeks to assess the effectiveness of the new approach. The active
investment started on 15/01/2022. Since the client has changed the investment decision and
chosen to invest in United States equity markets, the actively managed portfolio consists of 6
equities and 2 corporate bonds. After investing in the active portfolio, the remaining amount is
£1,024,513.39.
1.2.2 Asset Allocation
To compete in the different asset allocations, such as bond and equity, the author used a
diversified approach. Having a diversified approach helps in minimizing risk associated with the
investment (Hoevenaars, Molenaar, Schotman & Steenkamp, 2008). Stock and bond
performance will be tracked for a period of 10 weeks.
The active portfolio was constructed using a bottom-up approach. According to Clarke, de Silva
& Thorley (2016) stated that bottom-up approach tends to produce better performance results. As
well, Lee and Swaminathan (1999) claim that this approach is better for analyzing a company’s
performance within the market and focuses on technical analysis.
A tactical asset allocation portfolio (TAA) is used for the purpose of managing equity portfolios.
The objective of TAA strategies is to achieve a positive information ratio through systematic
asset allocation shifts (Lee, 2000), and attempts to obtain high returns while reducing risk by
monitoring the portfolio performance against a benchmark. In the active portfolio, the client has
selected stocks and corporate bonds from the US. Although, the S&P 500 index is used by the
active management team as a benchmark for the portfolio. As stated by Dahlquist & Harvey
(2001), the US business cycle can be predicted to a certain extent. However, the TAA process
performance of the stocks within the portfolio can be better predicted.
According to several studies, markets are highly fluctuated either experiencing positive or
negative changes. The investor may encounter both systematic and unsystematic risks when
investing in stocks according to Zaimovic, (2021). However, unsystematic risk is
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commonly known to as diversifiable risk. In order to reduce unsystematic risk, diversification
strategy should be applied to the investment portfolio (Ludan & Gary, 2018). Diversification
of the portfolio can be done by including equity and corporate bonds in the investment to
achieve maximum benefit (Fabozzi & Markowitz, 2011). In active portfolio, diversification
approach was applied within sectors, as the stocks and bond selection were based on US
market forecast.
A Markowitz Efficient Frontier tool can also be used to determine the most effective portfolio
that reduces risk while increasing returns. The theory explains how diversifying investments can
maximize future returns and minimize risks (Mangram, 2013). Therefore, investors should select
an appropriate portfolio combination in order to maximize their expected returns.
Figure 1. Markowitz Efficient Frontier.
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2.1 Management of the stocks and bond portfolio
2.2 Rebalancing Strategy
Rebalancing strategy involves buying and selling securities in order to realign its weights back to
its original (Dichtl, Drobetz & Wambach, 2016). The weights need to be rebalanced to avoid any
one asset dominating the portfolio, given the investor’s level of risk aversion. Rebalancing
strategy has the benefit of maintaining an investor’s original investment policy (O’Brien, 2006).
Perold and Sharpe (1988) suggested that in order to rebalance, investors should buy stocks and
sell bonds when stocks decline. Graham (1965) suggests that an investor taking moderately risky
decisions shouldn’t concentrate only on getting high capital gains, but should also focus on
selling them when they are profitable. In this situation, since the client takes moderate risks, it’s
best to avoid high risks. However, the active portfolio is composed of a diversified portfolio mix
of equity securities and corporate bonds, equally weighted and rebalanced based on market
movements. However, equally weighted portfolios outperform market capitalization-weighted
portfolios based on Carhart four-factor model (Urbán & Ormos, 2012).
2.2.1 Rebalancing 1: Dividend Discount Model (DDM) Week 2
The dividend discount model (DDM) is a method for predicting how much a company’s current
share price is worth when discounted back to its present value (Nagorniak, 1985). It is based
upon the theory that the stock’s present value is equal to the sum of all future dividend payments.
DDMs can indicate undervalued. By contrast, if the theoretical price from the DDM is higher
than the closing share price, this indicates an undervalued stock that should be purchased
(Nagorniak, 1985).
The DDM function was applied using Bloomberg to all six stocks (AMZN US, EOG US, FL US,
GOOGL US, V US, & X US). It was noticed that GOOGL US, V US and EOG US (refer to
figure 2,3 & 4) theoretical prices are higher than the closing price, which it indicates that the
stocks are undervalued. As a result of AMZN US, FL US and X US (refer to figure 5, 6 & 7),
their theoretical prices are lower than the closing price, which it indicates that the stocks are
overvalued. However, the client decided to sell only AMZN to buy another stock, and keep FL
and X US on hold for next rebalancing
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Figure 2. DDM – GOOGL US Equity
Figure 3. DDM – V US Equity
Figure 4. DDM – EOG US Equity.
Figure 5. FL US Equity DDM. From Bloomberg
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Figure 6. X US Equity DDM. From Bloomberg
Figure 7. AMZN US Equity DDM. From Bloomberg
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2.2.2 Rebalancing 2: Capital Asset Pricing Model (CAPM) Week 4
CAPM is the most widely used model, which is used to help an investor decide which
investments to make and which portfolios to invest in (Armstrong, 2008). CAPM aims to
quantify risk and translate that risk into an estimate of expected return on equity. CAPM can take
into account both the impact of risk and the impact of mispricing (Hirshleifer, 2001). However, it
can be used by financial managers as a supplement to other approaches and their own judgment
when developing realistic and useful cost of equity calculations (Wijaya, 2020).
!= “+ !( #– “)
Table 1. CAPM Stock Evaluation

Figure 8. Figure 2: Security Market Line

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According to the model, two stocks have overpriced and should be sold (table 1 & figure 2)
(Francis & Kim, 2013). Following that, the client decided to sell half of the share for two stocks
and keep them on hold till next rebalancing.
Figure 9. X US Equity Sell Ticket.
Figure 10. FL US Equity Sell Ticket.
2.2.3 Rebalancing 3: Relative Valuation Model (RV)
The relative valuation method (RV) compares a company’s stock price or other indicators such as
cash flow, book value, and ratios to those of its competitors or industry in order to determine its
financial worth (Damodaran, 2012). The model assumes that normal markets are priced
correctly, but individual stock prices might contain errors. Although the model is criticized for its
inaccuracy and inefficiency in the literature, it is termed as an effective method. As an
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alternative, the technique is relatively easy to apply and several multiples can be used to reduce
the estimation error. P/E ratios are one of the most common multiples used in relative valuation
(Voss & Larrabee, 2013). According to the literature, low P/E ratios are an indicator for good
future performance, and portfolios constructed by P/E can outperform benchmarks (Keown,
Pinkerton & Chen, 1987).
Table 2. Comparison of the P/E ratios of stocks in their respective industries.

Table 2 represent P/E ratio of each stock in comparison with their industries. the data extracted
from Bloomberg in week 5. Among the six stocks, two turn out to be overpriced compared with
their respective industries based on a comparison of their PE ratios. Following this, stocks with
the greatest P/E gap were sold, and their replacement was made by those with the greatest
P/E<industry. However, table 3 shows that the client replaced the two sold stocks and replace
them by buying three new stocks.
Table 3. Equity Rebalancing – Week 5

2.3 Bond portfolio Management
The bond was chosen based on the investor’s profile as a moderate risk-taker. Diversification was
the main objective when selecting corporate bonds from two different sector. In bond selection,
credit ratings play an important role. Credit rating agencies collect and analyze a variety of
information to determine creditworthiness (White, 2018). Using the Standard and Poor’s Global
Ratings as a benchmark was the traditional approach, however, to have the full picture of the
bond, Moody’s ratings had to be considered as well.
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Table 4. Corporate Bonds Credit Ratings

Table 4 shows that both CB are expecting a positive investment outlook. Microsoft 3.3 is rated as
the highest investment grade by both S&P and Moody’s. Comparing APPL 3.35 to MSFT 3.35, it
indicates that there might be defaults or low returns in the future.
Bond laddering is a strategy of diversification in which bonds are purchased at different maturity
dates in order to minimize the impact of changing interest rates. In this way, investors can react
directly to the change in interest rates. The convexity of the cash flows increases with this
approach, since the flows vary over different maturities (Cheung et al., 2010).
Figure 11. Changes of U.S. Bond Yield of February

Source: World Government Bonds (2022)
Campbell (1995) shows that bond yields increase as maturity time approaches which results in
higher yields (see figure 11). In reaction to changes in US bond yields, the investor sold APPL
bond and bought another bond with another maturity and sector to diversify. Active portfolio has
two US CP maturity dates ranging from 3 to 7 years.
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3.1 Portfolio Evaluation
The absolute performance of a passive and active portfolio is determined by calculating the loss
and gain of the investment (Table 5). It shows that passive delivers a higher return than active.
An outbreak of COVID-19 pandemic caused huge recession in the stock market, lowering the
return on active portfolios.
Table 5. Passive and Active Absolute Performance (Week 10 – 26 March 2022)

3.2 Active Portfolio Evaluation
Table 6 shows active portfolio performance measures which conclude a weak performance
against the benchmark. Negative Sharpe ratios signify lower investment returns than risk-free
rates in the portfolio. Jensen Alpha is negative, which means that the client did not earn enough
returns to compensate for the risks he took (Modigliani & Leah, 1997).
Table 6. Active Portfolio Performance Measures

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3.2 Statistical Summary
Figure 12. Active Portfolio Statistics – Return
In comparison to the benchmark S&P 500 index returns, the total/absolute return for the one month
period is 2.48%. It indicates the inadequacy of the selection of stocks using value investing principles
(Li et al., 2009). The portfolio’s maximum return exceeded the benchmark, indicating a more stable
market.
Figure 13. Active Portfolio Statistics – Risk
Compared with the benchmark, the annualized standard deviation of the portfolio is lower, indicating
that the return of the portfolio is more variable. Additionally, the portfolio’s annualized downside
risk is below the benchmark, meaning the portfolio is safer as a result of deviation above the mean.
Portfolio returns are negatively skewed at -0.18, which means they are less than the median or mode.
Figure 14. Active Portfolio – Performance Attribution Analysis
The above figure shows only portfolio return is negative. Due to Bloomberg’s inability to provide full
data, it is critical to compare the active return with benchmark.
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Figure 15. Passive Portfolio Statistics – Return
Figure 15 compares the total return of the passive portfolio to the benchmark WIG20 (Poland Stock
Exchange). Nevertheless, when looking at the last five years, the portfolio performed much better than
the benchmark and had good equity selection. As per value investing principles, higher returns can be
anticipated when a good selection of stocks is analyzed (Li et al., 2009). In comparison with the
portfolio, the benchmark forecasts show less volatility since they are lower in value.
Figure 16. Passive Portfolio Statistics – Risk
The Sharpe ratio (0.82) for the portfolio return for the 5 years is higher than the benchmark value,
reflecting its well-performed investments compared with the risk-free rate of return (Sharpe, 1965).
Figure 17. Passive Portfolio – Performance Attribution Analysis
As shown in figure 17, selection and allocation are two factors that contribute to an active return. The
allocation securities had a positive value, which means the equities were properly weighted. Further,
the value of the selected securities was positive, indicating a successful selection that translated into
good performance of the invested securities.
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Reference
Al-Aradi, & Jaimungal, S. (2018). Outperformance and Tracking: Dynamic Asset Allocation
for Active and Passive Portfolio Management. Applied Mathematical Finance., 25(3), 268–294.
https://doi.org/10.1080/1350486X.2018.1507751
Anadu, Kruttli, M., McCabe, P., & Osambela, E. (2020). The Shift from Active to Passive
Investing: Risks to Financial Stability? Financial Analysts Journal, 76(4), 23–39.
https://doi.org/10.1080/0015198X.2020.1779498
Armstrong, Frank, III. (2008). How much diversification is enough? Crafting a portfolio that
minimizes uncompensated risk. The CPA Journal (1975), 78(1), 48.
Azra Zaimovic, Adna Omanovic, & Almira Arnaut-Berilo. (2021). How Many Stocks Are
Sufficient for Equity Portfolio Diversification? A Review of the Literature. Journal of Risk and
Financial Management, 14(551), 551. https://doi.org/10.3390/jrfm14110551
Basu. (1983). The relationship between earnings’ yield, market value and return for NYSE common
stocks: Further evidence. Journal of Financial Economics, 12(1), 129–156.
https://doi.org/10.1016/0304-405X(83)90031-4
Baumohl. (2012). The secrets of economic indicators: hidden clues to future economic trends and
investment opportunities. FT Press.
Baumohl. (2010). Economic indicators that matter to investors (1st edition.).
Birchenhall, Jessen, H., Osborn, D. R., & Simpson, P. (1999). Predicting U.S. Business-Cycle
Regimes. Journal of Business & Economic Statistics., 17(3), 313–323.
https://doi.org/10.1080/07350015.1999.10524820
Bloomberg. (2022). https://www.bloomberg.com/news/articles/2022-01-12/u-s-inflation-showsmore-staying-power-after-hitting-7-in-2021. Bloomberg.com. Retrieved May 21, 2022, from
https://www.bloomberg.com/news/articles/2022-01-12/u-s-inflation-shows-more-staying-powerafter-hitting-7-in-2021
Campbell. (1995). Some Lessons from the Yield Curve. The Journal of Economic Perspectives,
9(3), 129–152. https://doi.org/10.1257/jep.9.3.129
Clarke, de Silva, H., & Thorley, S. (2016). Fundamentals of Efficient Factor Investing
(corrected May 2017). Financial Analysts Journal, 72(6), 9–26.
https://doi.org/10.2469/faj.v72.n6.3
Damodaran. (2012). Investment valuation : tools and techniques for determining the value of
any asset (3rd ed..). Wiley.
17
Dichtl, & Drobetz, W. (2009). Does tactical asset allocation work? Another look at the
fundamental law of active management. Journal of Asset Management, 10(4), 235–252.
https://doi.org/10.1057/jam.2009.6
Dichtl, Drobetz, W., & Wambach, M. (2016). Testing rebalancing strategies for stock-bond
portfolios across different asset allocations. Applied Economics, 48(9), 772–788.
https://doi.org/10.1080/00036846.2015.1088139
Erric Wijaya. (2020). Stocks Investment Decision Making Capital Asset Pricing Model
(CAPM). Jurnal Manajemen, 24(1), 93–108. https://doi.org/10.24912/jm.v24i1.621
Fabozzi, Markowitz, Fabozzi, Frank J, & Markowitz, H. (2011). The theory and practice of
investment management : asset allocation, valuation, portfolio construction, and strategies (2nd
ed..). Wiley.
Francis, & Dongcheol, K. /. (2013). Modern portfolio theory : foundations, analysis, and new
developments (1. ed.). Wiley.
Farrell. (1985). The Dividend Discount Model: A Primer. Financial Analysts Journal, 41(6),
16–25. https://doi.org/10.2469/faj.v41.n6.16
Graham, B. (1965). The intelligent investor. Prabhat Prakashan.
Hirshleifer. (2001). Investor Psychology and Asset Pricing. The Journal of Finance (New
York), 56(4), 1533–1597. https://doi.org/10.1111/0022-1082.00379
Hoevenaars, Molenaar, R. D. ., Schotman, P. C., & Steenkamp, T. B. . (2008). Strategic asset
allocation with liabilities: Beyond stocks and bonds. Journal of Economic Dynamics & Control,
32(9), 2939–2970. https://doi.org/10.1016/j.jedc.2007.11.003
Huang, & Jane, C.-J. (2009). A hybrid model for stock market forecasting and portfolio
selection based on ARX, grey system and RS theories. Expert Systems with Applications, 36(3),
5387–5392. https://doi.org/10.1016/j.eswa.2008.06.103
Keown, A., Pinkerton, J., & Chen, S. (1987). Portfolio Selection Based Upon P/E Ratios:
Diversification, Risk Decomposition and Implications. Journal of Business Finance &
Accounting, 14(2), 187-198.
Kristjanpoller, & Olson, J. E. (2015). The effect of financial knowledge and demographic
variables on passive and active investment in Chile’s pension plan. Journal of Pension
Economics & Finance, 14(3), 293–314. https://doi.org/10.1017/S1474747214000213
Lee, & Swaminathan, B. (1999). Valuing the Dow: A Bottom-up Approach. Financial Analysts
Journal, 55(5), 4–23. https://doi.org/10.2469/faj.v55.n5.2295
18
Lee, W. (2000). Theory and methodology of tactical asset allocation (Vol. 65). John Wiley
& Sons. Wiley & Sons.
Li, Brooks, C., & Miffre, J. (2009). The Value Premium and Time-Varying Volatility. Journal
of Business Finance & Accounting, 36(9-10), 1252–1272. https://doi.org/10.1111/j.1468-
5957.2009.02163.x
Ludan Theron, & Gary van Vuuren. (2018). The maximum diversification investment
strategy: A portfolio performance comparison. Cogent Economics & Finance, 6(1).
https://doi.org/10.1080/23322039.2018.1427533
Mangram, Myles E., (2013). A Simplified Perspective of the Markowitz Portfolio Theory
Global Journal of Business Research, v. 7 (1) pp. 59-70, 2013, Available at SSRN:
https://ssrn.com/abstract=2147880
Nagorniak. (1985). Thoughts on Using Dividend Discount Models. Financial Analysts
Journal, 41(6), 13–15.
O’Brien. (2006). Rebalancing: a tool for managing portfolio risk. Journal of Financial
Service Professionals, 60(3), 62.
Peterson. (2012). Investment theory and risk management (1. ed.). Wiley.
Pham, Wei, X., & Zhou, C. (2022). Portfolio diversification and model uncertainty: A
robust dynamic mean‐variance approach. Mathematical Finance, 32(1), 349–404.
https://doi.org/10.1111/mafi.12320
Puelz, Hahn, P. R., & Carvalho, C. M. (2020). Portfolio selection for individual passive investing.
Applied Stochastic Models in Business and Industry, 36(1), 124–142.
https://doi.org/10.1002/asmb.2483
Ranjith, V. K. (2002). Risk preference of investors in the city of Ahmedabad. Finance
India, 16(2), 531.
Sharpe. (1991). The Arithmetic of Active Management. Financial Analysts Journal, 47(1), 7–
9. https://doi.org/10.2469/faj.v47.n1.7
Statman. (1987). How Many Stocks Make a Diversified Portfolio? Journal of Financial
and Quantitative Analysis, 22(3), 353–363. https://doi.org/10.2307/2330969
Statista. (2022). Poland: GDP change 2021. Statista. Retrieved May 21, 2022,
from https://www.statista.com/statistics/1244907/poland-gdp-change/
Statista. (2022). Poland: Yearly CPI inflation rate 2021. Statista. Retrieved May 21, 2022,
from https://www.statista.com/statistics/1258363/poland-yearly-cpi-inflation-rate/
19
Voss, & Larrabee, D. T. (2013). Valuation techniques : discounted cash flow, earnings quality,
measures of value added, and real options. John Wiley & Sons.
White. (2018). The Credit Rating Agencies and Their Role in the Financial System. In The
Oxford Handbook of Institutions of International Economic Governance and Market Regulation.
Oxford University Press. https://doi.org/10.1093/oxfordhb/9780190900571.013.38
Zurek, & Heinrich, L. (2020). Bottom-up versus top-down factor investing: an alpha forecasting
perspective. Journal of Asset Management, 22(1), 11–29. https://doi.org/10.1057/s41260-020-
00188-9
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Source
Result
Reference
Standard Life Medium
Risk
https://retirementplans.vanguard.com/VGApp/pe/IQResults.jsf
Vanguard Moderate https://retirementplans.vanguard.com/VGApp/pe/IQResults.jsf
Bright Start Moderate https://ubt.wealthmsi.com/riskq.phtml?pid=BS
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Passive Portfolio
Market Value – Passive Portfolio
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Investor Profiling – Passive Portfolio

Sectors Analysis – Passive Portfolio
Passive Portfolio Allocation
Paasive Portfolio Allocation

Consumer Staples
Energy
Health Care
Industrials
Information Technology
Real Estate
69%
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Investor Profiling – Active Portfolio

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Market Value – Active Portfolio
Active Portfolio Allocation by attribution
Active Portfolio Allocation

Consumer discretionary was used, since it relied on products and services that supported the
needs of the population during the COVID-19 pandemic. Since everything has been online
during that time, investing in communication services sector for getting high returns is highly
efficient because most everything is online during that time, as well as the IT sector.
Active Portfolio – Asset Allocation
Based on the results of the risk-profiling questionnaire, Standard Life recommends an asset
allocation of 20% in stocks and 70% in corporate bonds for this client. However, the client
prefers to allocate 80% of their portfolio to stocks and 20% to corporate bonds.
Active Portfolio – Economic Indicator
Investors and clients benefit from market forecasts since they can discover any changes in the
market conditions that can have an impact on the market (Huang & Jane, 2009). An economic
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variable determines how the economy will perform in the future, and thus, its effect on the stock
prices of the selected companies. The COVID-19 outbreak affected all stock markets. In
comparison to previous years, the economy of the US did not perform well during this pandemic.
Many economic indicators showed negative effects on the stock market and selected companies,
such as the GDP, inflation rate, unemployment rate, and consumer price index (CPI).
US Economic Indicators.

Source: (Bloomberg Anywhere, 2022)
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