Investors try to maximise the return of their investment while minimising the risk. The only way of diversify the risk is holding their investments in different financial assets (securities) and in different countries. Different securities in the portfolio perform differently at any point of time if there is negative correlation between investment assets, thus the entire investments would not suffer the effect of any declining investment as it will be compensated by higher perform securities. By diversifying the investment assets internationally, the investors can reduce their investment risk further; this is because investors need not necessarily be relying on particular domestic economy.
The recent surge in international portfolio investment is due to overcoming the barriers in international investment such as taxation, capital market regulation, transaction costs and lack information of international capital market.
Globalisation; the world becomes shrinking and financial markets become easier to access efficient and effectively; as a result, many economies changing their macroeconomic policies such as creating double taxation treaty, lifting the barriers in foreign exchange transactions, creating supranational organisation ( European union, NAFTA, AFTA)and deregulates the capital markets to attract more foreign direct investment into the country.
Deregulation and liberalised capital markets enable the investors to hold more efficient investment portfolio beyond their nation by investing in different markets & different financial assets.
Advanced and third generation technology brings the world in a finger tips help the investors to access more information & bring down the transaction cost associated with the international capital markets. Due to the introduction of international investment assets such as international mutual funds, internationally cross listed stocks, country fund etc, there are higher choice of investment assets available to investors to achieve more diversified investment in their portfolio to reduce the risk.
Due to the above reasons, the international portfolio investment is increasingly day by day.
Question No2.
Security returns are found to be less correlated across countries than within a country. Why can this be?
The main reason for holding portfolio investment is to reduce or diversify the risk of returns from the investments. Investors can only reduce risk of their investments when the securities in the portfolio are less correlated; this is because the low return of one security will be compensated by another high performed security in the portfolio. Investors diversify their investment internationally with the intention to reduce the risk as much as possible rather than relying on domestically in fact; investors who diversify internationally may be able to achieve higher returns with a low risk than who diversify only domestically.
The security returns are less correlated internationally due to several factors such as economic, industrial structure, political, psychological and even institutional which differ country to country.
Economic factors such as inflation, interest rates, exchange rates, trade cycle of economy, economic development, endowment of country's assets (gold, oil) differ country to country. The negative effects of these economic factors on one security in the portfolio will be compensated by another security of portfolio in different country as economic factors differ country to country. For instance a fall in security prices in US due to financial crisis can be compensated by increases in security prices in China if the investor holds securities internationally. If the investor holds his or her investment portfolio within a single country, almost all the securities in the portfolio need to face the effects of these economic factors.
Political factor also determine the security returns, the government decision and government instability, political unrest, war, terrorism all affect the returns of securities. For instance, changing foreign trading regulation (allowing FDI in retail) in India affects the stocks in India and not affects the returns of German stock in the portfolio. If an investor holds securities in India only, his securities' return will be heavily affected (securities from same country are subjected to same government policy) than those who holds investment portfolio internationally.
Industrial structure is one of the factors directly link to the return of securities; the number and size distribution of firms and hence their influence on industry profitability, business policy, and public policy differ country to country. For instance, in well developed countries like US, UK there is large number of firms in the particular industry and equips well developed and advance technologies in their operation than those in developing countries like India, Pakistan, therefore holding portfolio within one country (developing country) produce less return due to higher risk of industrial structure than those who diversify risk of industrial structure internationally by holding international portfolio investments.
Relatively less correlation of international portfolio securities return suggest that investors can maximise their returns with less risk if they diversify their investment portfolio internationally rather than domestically.
Question No.3
Explain the concept of the world beta of a security
The total risk faced by an investor in securities can be divided into two categories such as specific risk and market risk; the risk that can be reduced through diversification is specific risk and the risk that will not be reduced by diversification is known as market risk. A measure of the volatility or systematic risk (market risk) of a security or portfolio against the whole market called bête (). It is a simple measure of individual stock relative to the overall risk of the stock market.
The concept of world beta is important to measure the world market risk (systematic risk) when investors hold their portfolio internationally. The world beta measures the sensitivity of the national market (returns in a country's stock) movement against the world market (stock returns) movements. National markets differ country to country according to the macroeconomic policies and political and economic conditions, it is important to understand the national markets in order to invest in their country. The world market risk is common to all countries (stock) which cannot be diversified and measured though world beta.
The world beta 1 indicates that the national stock market moves according to the world market movement. If the beta is less than 1 means the national market will be less volatile than the world market. If it is more than 1, the national market is more sensitive than the world market. For instance; if beta for UK market is .96 means that when the world security market goes up (down) by 10%, the UK market goes up (down) by 9.6% (-9.6%). Negative beta means when the world market has a downward movement, the particular country's national market (stock value) goes up. The world beta can be zero those stocks are risk free such as government treasury bills. Countries with high beta are supposed to high riskier but they provide high returns and vice versa.
World beta can be defined using the following formula.
World Beta = % Change in a Country's Stock Market
% Change in World Stock Market
Question No 4.
Explain the concept of the Sharpe performance measure.
Sharpe performance ratio is a commonly used measure of risk adjusted portfolio performance, developed by William Sharpe. This measure explains; whether an investment portfolio's success is due to the efficient fund management or undertaking excessive risk. This ratio is based on mean and standard deviation theory. Sharpe ratio can be calculated by dividing the risk premium (subtracting the risk free rate from the expected rate of return of the portfolio) divided by risk (standard deviation of the portfolio return). The important of this measure is; it adjusts portfolio performance for total risk rather than systematic risk (market risk). This measures portfolio performance against a series of security indices such as S&P500.
This can be calculated as follows
Portfolio Return (Rp) - Risk free return (Rf)
Sharpe ratio (SR) =
Portfolio Risk (f)
The greater the portfolio' Sharpe ratio, the better its risk adjusted performance and vice versa. A negative Sharpe ratio implies that an asset with less risk will perform better than the stock being analysed. The Sharpe ratio will be high if the portfolio's risk premium high while standard deviation is low (portfolio risk). However it is valid only for normal distribution, i.e. portfolio risk can be adequately measured by standard deviation. When return distribution are not in normal, the Sharpe ratio can lead to misinterpretation. Sharpe performance ratio is an important ratio measure risk adjusted portfolio performance.
Part B.
Question No 5.
A commodity trader believes that average volume of wheat he traded can be described by a Normal model with a mean of 32,000 metric tons and standard deviation of 2,500 metric tons.
If a client buys some bushels of his wheat, would it be reasonable for the client to hope that the transactions will reach 40,000 metric tons? Explain.
Based on the information provided,
The mean ( 32000
The standard deviation ( 2500.
The trade (x) 40000.
The probability for the trade reach 40000 can be calculated as follows.
X -
Z =
40000 - 32000
=
2500
= 3.200
Based on the normal distribution, z value of 3.200 is equal to 0.4993.
Based on the findings, there is only 0.07% of possibility expected to reach the 40000 metric ton of wheat. Therefore the majority (99.03%) assure that, it would not to reasonable to hope that the client's trade reach the volume of 40000 metric tons.
Approximately what fraction of the transactions can be expected to reach less than 30,000 metric tons?
In order to calculate the fraction of the transaction which reach less than 30000 metric tons, z value is an important measure.
X -
Z =
30000 - 32000
=
2500
= -0.8
Z value of 0.8 can be found in the normal distribution table, where it is 0.2881.
Based on the above findings, 21.19% would be expected to reach 30000 metric tons of transaction.
Approximately what fraction of these trades can be expected to reach between 30,000 and 35,000 metric tons?
The fraction of trade between 30000 and 35000 can be calculated with the z value. i.e,
30000 X
Calculate the test statistic Z equivalent to 30000 tons
X -
Z =
30000 - 32000
=
2500
= -0.8
Calculate the test statistic Z equivalent to 35000 tons
X -
Z =
35000 - 32000
=
2500
= 1.2
Therefore z value is p (-0.8)
When we look at the z value in the normal distribution is
p (-0.8 = 0.2881
p (1.2= 0.3849
Therefore p (-0.8
Based on the above calculation approximately 67.3% transaction reach between 30000 and 35000 metric tons.
Estimate the IQR of the trade volumes.
Inter quartile range (IQR) is mid spread; i.e. the differences between the 1st quartile (25th percentile) and the 3ed quartile (75 percentile).
In order to find the IQR of the trade value, we need to find the 1st quartile and 3ed quartile value of the trade.
By using the z value, Q1 and Q3 value of the trade can be calculated.
1st Quartile;
X -
Z =
X - 32000
-0.6714 =
2500
-1678.5 = X - 32000
X = 30321.5
3ed Quartile.
X -
Z =
X - 32000
0.6714 =
2500
1678.5 = X - 32000
X = 33678.5
Therefore inter quartile rage (IQR) = Q3 - Q1
= 33678.5 - 30321.5
= 3357 metric tons.
In planning an investment strategy, the commodity trader wants to offer an opt-out guaranty (or an option to cancel a trade) to any customer whose transaction volumes failed to deliver an agreed volume of transaction compared to the mean. However, he does not want to take too big a risk. If he is willing to give transaction refunds to no more than 1 of every 25 customers, for what volume level of transactions can he offer an opt-out guaranty?
Based on the information provided, the transaction refunds applied to every trade which fail to deliver the agreed volume of transaction compared to the mean. For 1 of every 25 transactions this refunds policy is applicable.
1 of every 25 transaction is (1/25) which represents 0.0400 of the normal distribution curve, therefore z value is based on normal distribution table is -1.751 ( 0.5000- 0.0400 = 0.4600)
Therefore z value is -1.751
Based on Z value, we can find the what volume level of transaction which can be offered for an opt out guaranty
X -
Z =
-1.751 = X - 32000
2500
-4377.5 = X -32000
X = 27622.5
Therefore, the trader can fixed the 27622.5 metric tons as the volume level of transaction to offer an opt out guaranty.
Question No 6.
In 1999, Lehman Brothers estimated that 48% of its investment bank traders took diverse forms of soft drugs. Based on these data, Lehman established a Drug Eradication Plan goal of reducing that figure to 16% by the year 2010. To that end, they hoped to achieve a reduction to 20% by 2006. In 2006, they released a research study in which 23% of a random sample of 1,815 traders said they were currently addicted. Is this evidence that progress towards the goal is off track?
Write appropriate hypotheses.
Null hypothesis (Ho): is the hypothesis that is to be tested. This is a proposition that is considered true unless the sample which is used to conduct the hypothesis tests gives convincing evidence that null hypothesis is false.
Based on the above statement,
Ho: 2; 20% of investment bank traders take drugs. (The progress of the Lehman Brother's Drug Eradication Plan towards its goal is on track)
Alternative hypothesis (Ha); is the hypothesis accepted when the null hypothesis is rejected based on the evidence.
Ha: 2 More than 20% of investment bank traders take soft drugs (The progress of the Lehman Brother's Drug Eradication Plan towards its goal is off track; i.e. Lehman Brothers plan to achieve 20% of Drug eradication in the year end of 2006, suppose if their fail to achieve this, the result of their progress is more than 20 %)
Upper tail test is suitable.
Verify that the appropriate assumptions are satisfied.
Generally hypothesis tests for proportion should meet the following condition
The sample should be taken randomly (the sampling method is simple random sampling). The research relating to progress of Lehman brother' drug eradication plan is conducted using the sample which is taken from the population. The sample amount is 1815 as stated in the question.
Each sample point can result in two possible outcomes; 'Success' (possess certain Characteristic) and 'Failure' (does not possesses that characteristic) Proportion of success indicate and the sample proportion indicates. Based on the above data and 1-
Both nand n (1- ) should be at least 5.
Based on the data given,
They are both greater than 5 (363+1452 = 1815), so the sample is large enough.
The above mention conditions have been satisfied; therefore a normal distribution with mean and standard deviation can be used to model the sampling distribution of proportion with
C) Find the p-value of this test.
Based on the above data, we can carry out one proportion Z test and the research shows the proportion of investment bank traders who are addicted to drug is (p) = 0.23 (23%)
Therefore, =
d). Explain what the p-value means in this context and set an appropriate conclusion - Of course, your conclusion may be incorrect and if so which kind of error did you commit?
The P value indicates that if the proportion of traders who are addicted to drugs is 20%, the probability that a sample of this size will be proportion of 23% or more is 0.007.
Therefore an appropriate conclusion is null hypothesis is rejected because P value is 0.0007 (0.07%) that mean there is no strong evidence to prove that the progress of the Lehman Brother's Drug Eradication Plan towards its goal is on track because it failed to achieve its target in the year of 2006 (more than 20% of traders took drugs in 2006).
If our conclusion is incorrect, that mean Ho is correct but we reject Ho and accept Ha, therefore it is type 1 error.
Question No.7
Of all the CEOs in the Citibank, Walter Wriston had the highest disapproval rating from the internal bankers near the end of his mandate. His disapproval rating was the highest at 66% in May 1973 during the oil crisis, before he resigned. In May 2007, Charles Prince's disapproval rating was 63%, according to an internal poll of 1,000 internal bankers. Bank experts started discussing whether Charles Prince's rating was still discernibly better than that of Walter Wriston's. What do you think?
Based on the information provided, we can carry out hypothesis test for proportions to check whether internal bankers' conclusion is acceptable or not.
Step 1; Develop an appropriate hypothesis.
H0; Charles Prince disapproval rate was 66% on May 2007.
Ha; Charles Prince disapproval raw less than 66%.
Step 2; Make sure the conditions for hypothesis test for proportion are met.
We assume that banker's responses are unbiased and bankers are randomly chosen.
Both nand n (1- ) should be at least 5.
Based on the data given,
They are both greater than 5 (660+340 = 1000), so the sample is large enough
The above mention conditions have been satisfied; therefore a normal distribution with mean and standard deviation can be used to model the sampling distribution of proportion with
,
Step 3; Find the P value;
Based on the data, we can do one proportion Z test. The observed proportion of disapproval rate (63%)
,
Therefore this proportion is -2.00 standard deviations below the hypothesized proportion of disapproval rate.
Thus p ( = 0.5-0.4783
= 0.0217.
Step 4; Conclusion.
Based on the above calculation our p value is 0.0217 (2.17%) which is very low therefore we reject the null hypothesis( Ho) and accept alternative hypothesis (Ha)That mean, there is strong evidence that Charles Prince's May 2007 disapproval rating was lower than 66%. Therefore Charles Prince's rating discernibly better than the disapproval rating of Walter Wriston's.
