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State whether the claim is true orfalse. Supply a brief explanationfor your answer

Geographic diversification always allows banks to increaseearnings and diversify risk.

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Irving Heathcote
Irving HeathcoteLv2
28 Sep 2019
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Hi guys could someone help me and explain in detail the two fundamental principles of investments – the risk/return tradeoff and diversification. Also, describe how asset allocation and the correlation of various securities within asset classes impact the riskiness of an investor’s portfolio.

I found an answer but it seems to me very long and not sure about it so can you help me out guys

ANS:

Risk /Return Tradeoff

Risk, return and liquidity are three dimensions of investment decision. Risk/Return trade off considers two dimension ie risk and return. As risk of an investment increases , its expected return will decrease. Risk is measured by volatility of return which can be statistically obtained by standard deviation of return. Higher the standard deviation, higher will be volatility of return and higher the risk

Risk can be also measured as a relative risk compared to the market. This is measured by stock beta with reference to a market index. Higher the beta, higher the value of stock Beta, higher will be the risk .

Investors seeking higher return will need to take higher risks.

Treasury bonds are almost risk free assets. This has the lowest rate of return. Stocks have higher risk , hence have higher expected return. High beta stocks will have higher risk and higher returns.

An investor should understand his risk taking ability and will have to make a trade off between risk and return depending on his risk apetite.

Diversification:

There is a saying, do not put all your eggs in one basket. The reason is that it has higher risk if all eggs are in one basket. If the eggs are distributed in different basket, risk of loss decreases.

Same principle is applied in investment. Diversification reduces risk.

If one invests in different classes of assets like bonds, stock, commodities and properties –his risk is likely to reduce. Reduction in return in one asset is likely to be compensated by return in other asset.

Within one class of asset also, there should be diversification to reduce risk.

For example one stock “A “may have expected return of 10% and standard deviation of 5%.This risk can be reduced by diversification in number of assets and the ratio of Risk/return can be decreased.

If we diversify and instead of investing 100% in stock A, we invest 60% in “A” and 40% in another stock “B” having expected return15% and standard deviation of 8%.assume the correlation between the two assets are 0.5

Portfolio return=wa*Ra+wb*Rb

Wa=Weight of asset A=0.6

Wb=Weight of asset B=0.4

Ra=Return of A=10%

Rb=Return of B=15%

Sa=Standard deviation of A=5%

Sb=Standard deviation of B=8%

Corr(a,b)=Correlation of A & B=0.2

Portfolio return=0.6*10+0.4*15=12%

Portfolio Variance=(wa^2)*(Sa^2)+(wb^2)*(Sb^2)+2wa*wb*Cov(a,b)

Cov(a,b)=Corr(a,b)*Sa*Sb=0.1*5*8=4

Portfolio Variance=(0.6^2)*(5^2)+(0.4^2)*(8^2)+2*0.6*0.8*4=23.08

Portfolio standard deviation=Square root of Variance=(23.08^0.5)=4.8%

The diversification has increased return and reduced risk

Stock A was giving 10% return with 5% standard deviation. With diversification of portfolio we have 12% return and 4.8% standard deviation. Risk return ratio is decreased.

It may be noted that, higher the correlation between assets in the portfolio, higher will be risk in terms of standard deviation. Hence it is better to diversify with uncorrelated assets.

Diversification reduces unsystematic risk,but it cannot reduce systematic risk of overall market or economy

Fill in the blank using a number of terms listed below (@1 point per question).

Beta coefficient, Bonds, CAPM, Cash flows, Change, CV, Convertible bonds, Correlation, Correlation coefficient, Debenture, Discount, Diversifiable risk, Expected return, Interest rate risk, Inverted, Junk Bonds, Market risk, More, Normal, Opposite, Probability distribution, Ratings, Reinvestment rate risk, Risk, Risk averse investor, Risk premium, Standard deviation

______________is the chance that some unfavorable event will occur. For instance, the risk of an asset is essentially the chance that the asset’s cash flows will be unfavorable or less than expected.

A __________________ is a listing, chart or graph of all possible outcomes, such as expected rates of return, with a probability assigned to each outcome.

The ______________________is a statistical measure of the variability of a set of observations. The variance of the probability distribution is the sum of the squared deviations about the expected value adjusted for deviation.

The _______________________ is equal to the standard deviation divided by the expected return; it is a standardized risk measure which allows comparisons between investments having different expected returns and standard deviations.

A _______________________ dislikes risk and requires a higher rate of return as an inducement to buy riskier securities. A realized return is the actual return an investor receives on their investment. It can be quite different than their _______________________.

A ________________ is the difference between the rate of return on a risk-free asset and the expected return on Stock i which has higher risk.

_________________ is a model based upon the proposition that any stock’s required rate ofreturn is equal to the risk free rate of return plus a risk premium reflecting onl y the risk remaining after diversification.

_________________ is the tendency of two variables to move together. A _________________ of +1.0 means that the two variables move up and down in perfect synchronization, while a coefficient of -1.0 means the variables always move in opposite directions.

_________________ is that part of a security’s total risk that cannot be eliminated by diversification. It is measured by the beta coefficient. _________________ is also known as company specific risk. This risk can be eliminated by proper diversification.

The _________________ is a measure of a stock’s market risk, or the extent to which the returns on a given stock move with the stock market.

Suppose that you are a bank regulator who knows that there are two types of banks under your jurisdiction, high quality (H) and low quality (L), who differ in their ability to screen loan applications for credit-worthy borrowers. Using past data you estimate that roughly 70% of banks are high quality and 30% are low quality. High-quality banks generate a cash flow per loan of 100k with probability .8 and 0 with probability .2. A low-quality bank on the other hand generates a cash flow per loan of 100k with probability .5 and 0 with probability .5.

These banks primarily make small loans to local businesses which creates a social benefit of 4% per dollar lent (i.e. if the bank lends $10 then the social benefit is 4%*$10). When a bank fails though, it generates a social cost of 15% per dollar of losses to the bank's creditors (i.e. if creditors lose $10 then the social cost is 15%*$10).

As a regulator you must choose a “capital requirement”, dictating how much the banks can borrow to make loans, in order to maximize the expected social value. Each loan costs $50k and generates the returns described above. Additionally, the banks start with $50k of their own money to invest. You, as the regulator, are debating whether to let the banks borrow money to issue 0, 1, or 2 additional loans. We assume the banks find it optimal to issue as many loans as possible but can only raise additional funds by borrowing. This means banks will always make at least 1 loan with their initial $50k and will make an additional 0, 1, or 2 loans with borrowed money depending on how much the regulator allows them to borrow. All loans generate the same cash flow (e.g. if the H-type makes 3 loans then with prob .8 each loan generates a cash flow of 100k and with .2 each loan generates a cash flow of 0. Similarly, if the L-type makes 3 loans then each loan generates a cash flow of 100k with prob .5 and each loan generates a cash flow of 0 with probability .5).

 

Question:

Assume the regulator knows which banks are H-type and which are L-type. What is the expected social value (i.e. social benefit minus expected social cost) if the regulator allows the H-type bank to borrow 0, $50k, or $100k to make additional loans? What bout the L-type bank? How much will the regulator optimally allow the H-type and L-type banks to borrow? (remember all bank always makes at least 1 loan, so they will either make 1, 2, or 3 loans depending on whether the regulator allows them to borrow 0, $50k, or $100k. Also note that the social cost only applies to borrowed money lost in default, not the bank’s initial $50k, and the social benefit applies to money lent, not the realized cashflow).

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