My classmates and I carried out a project for the Corporate Finance course. The assignment consisted in applying Corporate Finance logic and replicating a setting that was as similar to the professional context as possible. The project's aim is to put into practice concepts related to return, risk and future value of a lump sum investment as well as portfolio diversification.

1. Assessment and Feedback: Student Template
Student ID Number(s): 2520279, 2520289, 2520274, 2520242, 2520333, 2519975
Programme: Exchange semester
Module: LI Corporate Finance
Name of Tutor: Nicholas Carline
Assignment Title: Corporate finance group assignment, group 65
Date and Time of Submission: 8/12/2022
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3. 1) Without the need to do any computations, rank the five portfolios from likely greatest to
likely least risk. Explain your reasoning behind this ranking.
1. UK small market capitalisation stocks (from various industries)
2. UK large market capitalisation stocks (from various industries)
3. UK 10+ year investment grade corporate bonds (from various industries)
4. UK 10+ year government bonds
5. UK 3 month government bills
1.1 Bonds & Bills VS Stocks
Bonds and bills are considered to be less risky in comparison to stocks, due to the fact that they are
enforceable debt instruments. Shareholders are not guaranteed dividends or capital gain on their
holdings, while bonds, as well as bills, have fixed cash flows if the investment is kept until its
maturity date. In addition, bond issuers are either national governments or large corporations, meaning
that the risk of default generally is quite low (Hillier et al., 2020). If a company or government
defaults on their bonds or bills due to financial struggles, i.e in the case of bankruptcy for a private
listed company, bondholders have a stronger position in comparison to shareholders. This is due to the
fact that bonds are debt instruments, while stocks are equity holdings. When a company is liquidated,
holders of debt instruments will receive their financial compensation first, while shareholders will be
paid, proportionally to their holding, the residual of the liquidated assets after all debt has been settled.
The value of bonds and bills are generally speaking only affected by movements in the interest rates,
and the value and interest rate have a negative relationship when the interest rate is rising. In cases
where the investor chooses not to hold on to the instrument until its maturity date, the result can be a
negative return. As interest rates fluctuate with time, instruments of this category will be riskier with
an increased length of maturity. Governments, with their broad and diversified portfolio of cash
flow-sources, are generally only exposed to domestic- and international systematic risk, hence why
we chose to rank corporate bonds higher than government bonds (Hillier et al., 2020).
Regardless of the fact that government bonds are considered to have a low risk, they can still be
affected negatively by large financial events, such as e.g the Greek state's financial duress in the 2010s
(Trading Economics, 2022). The UK 3 month government bills are therefore placed at number five as
the time horizon for the investment is significantly lower than that of the UK 10+ year government
bonds, thus exposing them to less risk associated with time.
1.2 UK Small Market Capitalisation Stocks
The relatively small size of these companies, compared to larger companies, makes them more
vulnerable to changing economic conditions. These factors could be different types of economic
crises, but also i.e legal prosecution or loss of key clients. Smaller companies are also less likely to get
access to credit in times of crisis, due to them being generally less financially resilient . Furthermore,
having the ability to issue bonds or other securities is not as common for small companies (Hillier et
al., 2020). Thus, we argue that they are the riskiest option in regard to the points brought forward.
1.3 UK Large Market Capitalisation Stocks
In contrast to the small market capitalisation stocks, this portfolio is expected to be less volatile due to
greater resilience to fluctuations in the overall economy. This is attributed to their generally larger
financial circumference and portfolio, giving them options to divest or use retained cash flows from
other parts of the company to cover up for struggling subsidiaries. The sheer size and financial

4. resilience of companies also make them less impacted by volatility in the financial system, as a lot of
their loans usually have lower interest rates, and they have the option to issue debt instruments to raise
capital (Hillier et al., 2020).
2) Which of the five portfolios will you choose to invest in? Explain your reasoning for selecting
this portfolio.
As there is almost always a risk associated with investments, the selection of a portfolio will
ultimately depend on the person's risk preferences. Assuming that the person will invest in a portfolio
on the capital market line, his internal characteristics will determine where on the line he wants to be
(Hillier et al., 2020). A higher expected return on assets will implicate a larger risk and the investor
faces a trade-off between the two. The person in this case is a 45-year-old with a good job who
receives money as a gift, which might make him willing to take on more risk. On the other hand,
having two kids might make him have a higher aversion to risk, since it is often associated with cash
outflows related to e.g future education. The investment time horizon is another factor that has to be
taken into account. The money will remain in the portfolio for 20 years, meaning that the person will
be 65 years old and heading for retirement when possibly getting rid of the financial assets. Since a
longer investment horizon makes you less sensitive to fluctuations on the financial markets, taking on
a larger risk by investing in the portfolio of large stocks makes sense in this case. Alongside, we
assume that the expected return of this investment won’t be crucial for his future economic well being,
seeing as he has a good job and most likely has his pension plan sorted out.
Overall, we assume that the person's goal of investment is capital appreciation, hence he should invest
in large stocks since it most likely will achieve capital growth, but with a lower expected risk than that
of the portfolio of small stocks.
3) You invest the gift money at the end of Q4 2000. Based on the portfolio that you have chosen
in part 2, what is the future value of your £20,000 lump sum investment by the end of
Q2 2021? (Show all your workings.)
We calculated the nominal future value of the portfolio of in the following order:
The quarterly return in percentages for all stocks was calculated by using the formula below:
Quarterly return =
𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑠𝑡𝑜𝑐𝑘 𝑣𝑎𝑙𝑢𝑒 𝑄𝑥
− 𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑠𝑡𝑜𝑐𝑘 𝑣𝑎𝑙𝑢𝑒 𝑄𝑥−1
𝐼𝑛𝑑𝑖𝑣𝑖𝑑𝑢𝑎𝑙 𝑠𝑡𝑜𝑐𝑘 𝑣𝑎𝑙𝑢𝑒 𝑄𝑥−1
Thus, we got the quarterly return for each stock for the entire period, 2000 Q4 to 2021 Q2.
We then weighted all individual stocks by portfolio share (Appendix, Q3.1), and multiplied the
weighted size of each individual stock with its respective quarterly return plus 1.
𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑟𝑒𝑡𝑢𝑟𝑛 = 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑠ℎ𝑎𝑟𝑒 𝑆𝑡𝑜𝑐𝑘 𝑖 𝑄𝑥−1
· (1 + 𝑄𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑟𝑒𝑡𝑢𝑟𝑛 𝑆𝑡𝑜𝑐𝑘 𝑖 𝑄𝑥
)
The weighted quarterly returns were summarised to get the single return for the portfolio during the
quarter (Appendix, Q3.2). This was then done for all quarters during the holding period.
The future value of the invested amount was computed quarterly by using the following formula:
𝐹𝑢𝑡𝑢𝑟𝑒 𝑣𝑎𝑙𝑢𝑒 𝑜𝑓 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 = 𝑃𝑉𝑥−1
· 𝑆𝑖𝑛𝑔𝑙𝑒 𝑟𝑒𝑡𝑢𝑟𝑛 𝑜𝑓 𝑡ℎ𝑒 𝑒𝑛𝑡𝑖𝑟𝑒 𝑝𝑜𝑟𝑡𝑓𝑜𝑙𝑖𝑜 𝑓𝑜𝑟 𝑄𝑥

5. The present value used in the first calculation is 20,000 which is invested in Q4 2000. For the
following quarters, the resulting future value was used to calculate the ‘year after’ starting value
before capital gains. This procedure was repeated until the last quarter in 2021.
By using the process outlined, we get the future value of the UK large market capitalisation stocks at
Q2 2021, which is £117,529.79.
4) Were you to have instead chosen to invest in one of the other (four) portfolios, what would the
future value of your £20,000 lump sum investment have been by the end of Q2 2021 for each of
these portfolios? (Show all your workings.)
We calculated the future value of the remaining portfolios following a similar procedure as in the
previous question. For the small stocks portfolio, the steps were the same, but when calculating the
future value of the portfolios with bonds and bills, there was no need for weighting as they were
presented combined. The return index could be used to calculate the return and then the quarterly
future value of the portfolios could be computed as presented in table 4.1.
Table 4.1 The future value by the end of Q2 2021 of the invested lump sum of £20,000 in the remaining
portfolios.
5) Graph the quarterly movements in the future values for each of the five portfolios over the
entire investment period. Do you regret having chosen the portfolio that you did in part 2?
Figure 5.1 Quarterly future values for each of the five portfolios from Q4 2000 to Q2 2021.
Large stocks have a final future value of £117,529.79, meaning that an investor keeping his money in
the portfolio over the whole period obtains 5.88 times the initial portfolio value. In addition, the
average quarterly return is positive and equal to 2.45%. However, by investing in small stocks, he
would have been able to obtain a higher return. Small stocks have a final future value of 1,047,678.69
(table 4.1), almost nine times the future value of the large stocks portfolio. Though, the standard
deviation, which can be used to represent the risk of the investment, has to be taken into consideration
as well. The large stock portfolio had a standard deviation of 7.45% compared to the small stocks
portfolio, which had 10.97% (table 7.1). If we had invested in bills or bonds the investment would
have been less risky as seen in table 7.1, but in addition considerably less profitable.

6. Altogether, we believe that the portfolio we selected is the most suitable based on the person's internal
characteristics. The person has a well-paid job, but in order to ensure a certain amount of money and
satisfy the needs of his children, the investment has to have an appropriate level of risk.
6) Construct and chart a quarterly return frequency distribution for each of the five portfolios
over the entire investment period. Do these distributions resemble a normal distribution?
Explain.
If we compare similar categories of
securities, starting off with small
and large stocks, we see in figure
6.1, that both frequency graphs are
quite close to normal distribution.
The portfolio of large stocks has less
of a spread in the sample and
therefore less volatility, than the
portfolio of small stocks. Figure 6.1
shows that both of the portfolio's
returns are skewed. The portfolio of
large stocks are positively skewed,
meaning that returns above the
mean, 2,45% (table 7.1), are more
varied but less frequent in their
specific return repetitiveness. The
portfolio of small stocks on the
other hand, are only somewhat
negatively skewed in its
distribution, implying high
variability but low repetitive
frequency in the specific returns
below the mean.
Figure 6.1 The quarterly return frequency distribution for each
portfolio.
When looking at the graphs, it is clear that stocks as a category have a higher standard deviation
through the tailedness of the distributions in comparison to bonds and bills, implying higher volatility.
Both portfolios of stocks have somewhat frequent outliers in comparison to the portfolios of
corporate- and government bonds and bills, resulting in a higher kurtosis. The portfolios of bonds and
bills have samples that are more centralised around the mean, resulting in a lower volatility (table 7.1)
Thus it can be concluded from the graphs that all securities are biased towards positive return when
analysing the historical data, as all means are positive. What is surprising, is that corporate bonds have
a lower kurtosis according to figure 6.1, and thus should be considered less volatile in comparison to
government bonds. One can also determine that bonds have not been skewed in their returns during
the time period as both sides of the mean are pretty symmetrical.
Analysing the portfolio of government bills, we see that the distribution is positively skewed. The
conclusion that can be drawn from this is that the portfolio of government bills has a high frequency
of returns between 0,0% up to its mean of 0,58% (table 7.1), but the positive returns above the mean
are more varied. Another important conclusion is that the volatility of returns of treasury bills is
significantly lower than if we compare it to stocks and government bonds, as shown in the graph with

7. the returns only varying between 0,0% and a little more than 1,5% at the extreme points of the normal
distribution.
7) Compute the arithmetic mean and the standard deviation of the quarterly returns for each of
the five portfolios over the entire investment period. (Show all your workings.) Tabulate and
graph your results. How do these results compare to your ranking based on risk in part
1? What do you conclude about return and risk?
The following formulas were used to compute the arithmetic mean and standard deviation.
Mean ( ) = Standard Deviation (𝝈) =
𝑟
(𝑅1
+ ... +𝑅𝑖
)
𝑛
1
𝑛 − 1
𝑖 = 1
𝑛
∑ (𝑟𝑖
− 𝑟)
2
Table 7.1 Mean and standard deviation of the quarterly returns for each of the five portfolios.
According to the risk-return tradeoff, the expected return increases with a rise in risk. Our results in
table 7.1 demonstrate a positive relationship between the risk and return of our portfolios with one
exception, the portfolio of corporate bonds, which also makes our result differ slightly from our
ranking. The risk of the portfolio of government bonds turned out to be higher than the risk of the
portfolio of corporate bonds, but with a lower return. As generally, corporate bonds are considered
riskier, this could potentially be due to historical contingencies affecting the volatility of the return of
government bonds to a greater extent than corporate bonds. Limitations in analytical accuracy in our
analysis is another possible cause. Overall, the risk-return trade-off was respected.
Figure 7.1 Mean and standard deviation of the quarterly returns of each portfolio.

8. 8) Graph the quarterly returns for each of the five portfolios over the entire investment period.
What do you conclude about risk? Using Library online databases and/or the World
Wide Web, identify and reference some macroeconomic news that likely accounts for the
three largest peaks/troughs in the quarterly returns history for the large stocks portfolio only.
Figure 8.1 The quarterly returns for each of the five portfolios from Q4 2000 to Q2 2021.
The downturn in the quarterly return of the portfolio of large stocks in mid to late 2002 can be
explained by a number of global events that shattered the confidence of investors in a climate of rising
political tension. In 2002 the lingering effect of the “dot.com bubble bust” was still in effect mainly
affecting the telecom- and technology sectors. At the same time, the world was still recovering after
the effects of the 9/11 attacks the year before and the eyes were on another possible invasion of Iraq.
This was further exacerbated by a fluctuating oil price affecting stock markets globally (Burrows,
2005).
The financial crisis 2006-2009 is likely to account for the largest peak seen in figure 8.1. The crisis
developed gradually and can be considered to have begun in the early 2006 when house prices started
falling, making many borrowers default on payments on their loans. The US financial institutions had
a high risk exposure due to their holdings of CDO’s, who had been seen as a stable and profitable
pack of MBS. The crisis eventually reached the rest of the world as Lehman Brothers went bankrupt
in 2008, which threatened international holding in the US. Meanwhile, banks from Asia and Europe
were exposed to the risk of the CDO’s as well (Wigmore, 2021).
As seen in figure 8.1, the quarterly return makes a deep dive in Q3 2015. This is possibly primarily
because the Shanghai composite index started falling in June and then fell by 8.5 percent in one day in
August, causing share prices around the world to go down as people feared that the Chinese economy
was going downhill (Hellier, 2015).
Seeing as bonds and bills are fixed-income securities, it is of no surprise that larger fluctuations are
seen in the returns of stocks as a result of these events. Stocks are largely dependent on investors
speculations and macroeconomic- & political events that influence confidence in the financial market.

9. 9) You have so far not taken inflation into consideration. Using the data provided for the
consumer price index, compute the average quarterly inflation rate over the entire investment
period. (Show all your workings.) Based on the arithmetic means of the nominal quarterly
returns that you have computed in part 7, did all five of the portfolios earn on average a real
quarterly return that exceeded inflation? What do you conclude?
Given the Fisher equation, which is , where i is the nominal rate, r is the real rate and
𝑖 = 𝑟 + π π
is the inflation rate, we are able to find the real quarterly mean return. We first found each quarterly
inflation rate by using this equation, where CPI is the consumer price index:
𝑄𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑖𝑛𝑓𝑙𝑎𝑡𝑖𝑜𝑛 𝑟𝑎𝑡𝑒 =
𝐶𝑃𝐼𝑋
− 𝐶𝑃𝐼𝑋 − 1
𝐶𝑃𝐼𝑋 − 1
Once we had obtained the quarterly inflation rate for the 20 years we computed the arithmetic mean to
find the average quarterly inflation rate. We then got the mean of real quarterly return for each
portfolio by subtracting the average quarterly inflation rate from the mean of the nominal quarterly
returns.
Table 9.1 Average quarterly inflation rate.
Table 9.2 Mean of the nominal quarterly returns and real quarterly returns of all portfolios.
All five of the portfolios earned, on average, a real quarterly return that exceeded inflation, but the
inflation reduced the returns by 0.51%, resulting in an almost non existing return on the bills portfolio.
Looking at the portfolio of government and corporate bonds in table 9.2, the inflation represents about
a half and a third of the nominal quarterly return respectively. For small and large stocks, the return
remains relatively high.
Overall taking inflation into consideration, the portfolio of bills is hit the hardest as its nominal return
was the lowest, making this an unsuitable investment for someone who wants to achieve capital
growth rather than only shielding money against inflation. Bond portfolios allow for some return, but
there is still a significant difference in particular to the portfolio of small stocks which has a real
quarterly return of 4,96% (table 9.2).
10) Assuming that the least risky of the five portfolios, based on what you have found in part 7,
can for all intents and purposes be regarded as a risk-free investment, and ignoring inflation,
compute and tabulate the arithmetic mean of the quarterly risk premium (return in excess of
the risk-free return) for each of the other (four) portfolios. (Show all your workings.) What do
these results tell you?
Based on the standard deviation of the portfolio of government bills, it is the least risky investment
and its return will be regarded as risk-free. As shown in table 7.1 it has a standard deviation that is
considerably lower than the one of the remaining portfolios.

10. To calculate the quarterly risk premium we used the following formula where is our computed
𝑟
average quarterly return and is our risk-free rate.
𝑟𝑓
=
𝑄𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚 𝑟 − 𝑟𝑓
Table 10.1 The average quarterly return of the government bills portfolio regarded as our risk-free rate.
Table 10.2 The mean of nominal quarterly return and arithmetic mean of the quarterly risk premium.
The results in table 10.2 confirm the risk-return trade-off theory. An investor taking on more risk, will
be obtaining a larger return. Although, as we already know from question 7, the government bond is
an exception in our case.
​
​
11) Perhaps by utilising some of what you have found from the above historical and
quarterly analysis, and again ignoring inflation, provide an estimate of the expected and
annualised risk premium from the end of Q2 2021 until the end of Q2 2023 for each of
the five portfolios. (Show all your workings, and state all assumptions that you make.)
According to the expected and annualised risk premium formula:
EARP t + 1 = (1 + 𝑄𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑟𝑖𝑠𝑘 𝑝𝑟𝑒𝑚𝑖𝑢𝑚)
𝑛
− 1
We are considering an interval of four quarters so n is equal to four:
Table 11.1 The expected and annualised risk premium for each of the five portfolios.
We computed the EARP (Q2 2021 - Q2 2022) by utilising the formula presented above. Subsequently,
we calculated EARP (Q2 2021 - Q2 2023) this way:
EARP (2021-2023) = (1 + EARP (2021-2022) ) 2
- 1
Assuming that the quarterly risk premium remains the same in 2022 and in 2023, since it was
computed with the average of returns and represents an insight of investors' risk appetite, we found
the expected and annualised risk premium according to the formula presented above. We are assuming
that, within the period considered, market conditions linked to the returns, stay constant. These
assumptions are supported by the fact that we are considering a very short time period which means
that presumably investors' risk appetite as well as macroeconomic variables do not fluctuate much.
Generally, the approach utilised to calculate the historical risk premium involves longer time horizons.
However, this approach has been subject to some criticisms because it does not consider all market
changes.

11. References
Burrows, D. (2005) The fall and rise of the Footsie Available at:
https://www.thisismoney.co.uk/money/markets/article-1593716/The-fall-and-rise-of-the-Footsie.html
(Accessed: 2 December 2022)
Hellier, D. (2015) ‘Five factors that shook the world’s markets in 2015’, The Guardian (27 Dec).
Available at:
https://www.theguardian.com/business/2015/dec/27/five-factors-shocked-stock-markets-2015
(Accessed: 29 November 2022)
Hillier, D., Ross, S., Westerfield, R., Jaffe, J., Jordan, B. (2020) Corporate Finance. 4th European
edn. London: McGraw-Hill Education
Trading Economics, (No Date) Greece Government Bond 10Y. Available at:
https://tradingeconomics.com/greece/government-bond-yield (Accessed: 7 December 2022)
Wigmore, B. (2021) The financial crisis of 2008 : a history of US financial markets 2000-2012.
Cambridge : Cambridge University Press

12. Appendix
Question 3
1. 𝑄𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑚𝑎𝑟𝑘𝑒𝑡 𝑠ℎ𝑎𝑟𝑒 =
𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑠𝑎𝑡𝑖𝑜𝑛 𝑋
𝑖=1
𝑛
∑ 𝑀𝑎𝑟𝑘𝑒𝑡 𝑐𝑎𝑝𝑖𝑡𝑎𝑙𝑖𝑠𝑎𝑡𝑖𝑜𝑛 𝑋
2. Total weighted quarterly return =
𝑖=1
𝑛
∑ 𝑊𝑒𝑖𝑔ℎ𝑡𝑒𝑑 𝑞𝑢𝑎𝑟𝑡𝑒𝑟𝑙𝑦 𝑟𝑒𝑡𝑢𝑟𝑛
Question 6
The quarterly return frequency distribution for each portfolio.