Answer to Question #276501 in Statistics and Probability for james

Question

The following information relates to stocks X, Y and Z on 1 July 2020:

Stock Number of Shares Price (Sh.)

X 60,000 30

Y 200,000 25

Z 90,000 65

During the year, stock X undertook a reverse stock split of one for two. On 1 July 2021 the prices of stock X, Y and Z were Sh. 40, Sh. 35 and Sh. 70 respectively

Required:

a) Construct a price weighted index for the three stocks and compute the percentage change in the index (3 mks)

b) Construct a value weighted index for the three stocks and compute the percentage change in the index (3 mks)

c) Discuss four key market anomalies (2 mks)

d) Discuss four costs incurred by investors for exclusion of financial services (2 mks)

Answer 1

a)

price weighted index:

on 1 July 2020:

stock X: $30/(30+25+65)=30/120=0.25$

stock Y: $25/(30+25+65)=25/120=0.21$

stock Z: $65/(30+25+65)=65/120=0.54$

on 1 July 2021:

stock X: $40/(40+35+70)=30/120=0.28$

stock Y: $35/(40+35+70)=30/120=0.24$

stock Z: $70/(40+35+70)=30/120=0.48$

percentage change in the index 

stock X: $(0.28-0.25)/0.25=0.12=12\%$

stock Y: $(0.24-0.21)/0.21=0.14=14\%$

stock Z: $(0.48-0.54)/0.54=-0.11=-11\%$

b)

values on 1 July 2020:

stock X: $60000\cdot30=1800000$

stock Y: $200000\cdot25=5000000$

stock Z: $90000\cdot65=5850000$

values on 1 July 2021:

stock X: $60000\cdot40=2400000$

stock Y: $200000\cdot35=7000000$

stock Z: $90000\cdot70=6300000$

value weighted index on 1 July 2020:

stock X: $1800000/(1800000+5000000+5850000)=0.14$

stock Y: $5000000/(1800000+5000000+5850000)=0.40$

stock Z: $58500000/(1800000+5000000+5850000)=0.46$

value weighted index on 1 July 2021:

stock X: $2400000/(2400000+7000000+6300000)=0.15$

stock Y: $7000000/(2400000+7000000+6300000)=0.45$

stock Z: $6300000/(2400000+7000000+6300000)=0.40$

percentage change in the index:

stock X: $(0.15-0.14)/0.14=0.07=7\%$

stock Y: $(0.45-0.40)/0.40=0.125=12.5\%$

stock Z: $(0.40-0.46)/0.46=-0.13=-13\%$

c)

Mispricing:

deviations from a benchmark theory of asset prices;  deviation relative to the benchmark.

The most common benchmark is the CAPM (Capital-Asset-Pricing Model). The deviation from this theory is measured by a non-zero intercept in an estimated security market line

Unmeasured risk:

anomaly may generate expected returns beyond those measured using the CAPM regression because the time-series of its returns are correlated with labor income, which is not captured by standard proxies for the market return

the most well-known example of this unmeasured risk explanation: "if assets are priced rationally, variables that are related to average returns ... ..., must proxy for sensitivity to common (shared and thus undiversifiable) risk factors in returns. The [3-factor model] time-series regressions give direct evidence on this issue

Limits to arbitrage:

Anomalies are almost always documented using closing prices from the CRSP dataset. These prices do not reflect trading costs, which can prevent arbitrage and thus the elimination predictability. Moreover, almost all anomalies are documented using equally-weighted portfolios, and thus require trading of illiquid (costly-to-trade) stocks.

The limits to arbitrage explanation can be thought of as a refinement of the mispricing framework. A return pattern only offers profits if the returns it offers survives trading costs, and thus should not be considered mispricing unless trading costs are accounted for.

Selection bias:

The documented anomalies are likely the best performers from a much larger set of potential return predictors. This selection creates a bias and implies that estimates of the profitability of anomalies is overstated. This explanation for anomalies is also known as data snooping, p-hacking, data mining, and data dredging, and is closely related to the multiple comparisons problem.

Most research on selection bias in market anomalies focuses on particular subsets of predictors. For example, calendar-based anomalies are no longer significant after adjusting for selection bias. A recent meta-analysis of the size premium shows that the reported estimates of the size premium are exaggerated twofold because of selection bias

d)

Financial exclusion is when people are unable to access financial services such as current accounts, savings accounts and other beneficial financial services as they are deemed to be too high risk. There are many negative effects of this exclusion, and it generally means that people become unable to remove themselves from poverty.

Lack of Access to IT:

Many people find themselves financially excluded because they are unable to maintain an IT presence and do not understand how to access finance online such as online banking. This trend seems to impact those over 65 more as they are not used to online systems and need support to relearn this method of banking.

Lack Of Products That Suit All Customers:

Another cause of financial exclusion is a genuine lack of financial services for people who do not fit a mainstream financial profile. A lack of insurance, credit and day to day banking facilities stops those who want to access services from getting them. This then means that it becomes very difficult to improve its financial profile and become included.

Social Exclusion:

Social exclusion is a very common cause of financial exclusion. This is when people who are unemployed, financially dependent on another person or who have no credit history in the country they reside in becoming financially excluded due to their social status. It is also very common for people who have migrated to a new country to become financially excluded in their new country.

Low Income:

It is widely believed that a low income is directly related to those people who are completely financially excluded. People who are on benefits have low paid cash-in-hand jobs, single parents and those with a disability often find themselves in the low-income bracket. This makes them less desirable to mainstream banking, and so it becomes virtually impossible to gain access to financial products.