risk and returns acc09 financial management part 2

RISK AND RETURNSRISK AND RETURNS

ACC09 FINANCIAL MANAGEMENT PART 2

2

The Risk Management The Risk Management FunctionFunction

• Managing firms’ exposures to all types of risk in order to maintain optimum risk-return trade-offs and thereby maximize shareholder value.

• Modern risk management focuses on adverse interest rate movements, commodity price changes, and currency value fluctuations.

© 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly accessible Web site, in whole or in part.

EFFECT OF MARKET DIVERSIFICATION TO FIRM-SPECIFIC

AND MARKET RISKS

Risk-Return Trade-offRisk-Return Trade-off


TWO BASIC RULES IN BASIC RISK MANAGEMENT• REQUIRE RETURNS AT LEAST

EQUAL TO THE RISK ONE IS WILLING TO TAKE.

• TO MEASURE RISK IS TO MEASURE RETURN

EXPECTED VALUE OF RETURNS

• describes the numerical average of a probability distribution of estimated future cash receipts from an investment project

EXPECTED VALUE OF RETURNS• Estimating the various amounts of cash

receipts from the project each year under different assumptions or operating con ditions

• Assigning probabilities to the various amounts estimated for one year, and

• Determining the mean value. The expected present value of all, future receipts could then be determined by summing the expected dis counted value of all years.

EXPECTED VALUE OF RETURNS

• The GREATER the Expected Value or Pay-off, the BETTER.

MEASUREMENTS OF RISK

• Variance • Standard Deviation (SD)• Coefficient of Variation (CV)• Beta• Covariance

The Variability of Stock The Variability of Stock ReturnsReturns

• VarianceVariance ( (22)) – a measure of volatility in units of percent squared

Normal distribution can be described by its mean and its variance.

1

)(Variance 1

2

2

N

kkN

tt

• Standard deviationStandard deviation – a measure of volatility in percentage terms

Variancedeviation Standard © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly

accessible Web site, in whole or in part.

FOR UNGROUPED

DATA


• VarianceVariance ( (22) ) – a measure of volatility in units of percent squared

Normal distribution can be described by its mean and its variance.

N

ttt Pkk

1

2/12

2

))((Variance

• Standard deviationStandard deviation – a measure of volatility in percentage terms

Variancedeviation Standard © 2012 Cengage Learning. All Rights Reserved. May not be scanned, copied or duplicated, or posted to a publicly

accessible Web site, in whole or in part.

FOR FOR GROUPED GROUPED

DATADATA

EXERCISE 1EXERCISE 1

• The following table summarizes the annual re turns you would have made on two companies: – One, a satellite and data

equipment manufacturer, and – Two, the telecommunica tions

giant, from 200A to 200J.


Year ONE TWO Year ONE TWO

Year ONE TWO

200A200A 80.95 58.26 200E 200E 32.02 2.94 200I200I 11.67 48.64 200B200B -47.37 -33.79 200F200F 25.37 -4.29 200J 200J 36.19 23.55200C200C 31.00 29.88 200G200G -28.57 28.86 200D200D 132.4 30.35 200H 200H 0.00 -6.36

Estimate the EXPECTED RETURN, VARIANCE, and STANDARD DEVIATION in annual returns in each company

Portfolio EV, Variance, Portfolio EV, Variance, and SDand SD

• The expected return is equal to the WEIGHTED AVERAGE returns of the assets in the portfolio.

• The variance of a 2-asset portfolio is equal to

• =wi2 (σi) 2 + w2

2 (σ2) 2 + 2 (wi)(σi) (w2)(σ2) ((rr22))

• =wi2 (σi) 2 + w2

2 (σ2) 2 + 2 (wi) (w2)(Cov)(Cov)

• The SD is equal to the square root of the variance of the portfolio.

The Relationship Between Portfolio The Relationship Between Portfolio Standard Deviation and the Number Standard Deviation and the Number

of Stocks in the Portfolioof Stocks in the Portfolio

• The risk that diversification eliminates is called unsystematic risk; The risk that remains, even in a diversified portfolio, is called systematic risk.


What really matters is What really matters is systematicsystematic risk….risk….

how a group of assets move together.how a group of assets move together.

Market rewards only Market rewards only systematic risk.systematic risk.

The trade-off between S.D. and average returns that holds for asset classes does not hold for

individual stocks!


• CV = Standard Deviation = Standard Deviation• Mean Return Expected Return

• Coefficient of Variation Coefficient of Variation (CV) (CV) – a better measure of total risk than the standard deviation, especially when comparing investments with different expected returns


• Recall: • The variance of a 2-asset portfolio is equal to

• =wi2 (σi) 2 + w2

2 (σ2) 2 + 2 (wi)(σi) (w2)(σ2) ((rr22))

• =wi2 (σi) 2 + w2

2 (σ2) 2 + 2 (wi) (w2)(Cov)(Cov)

• How would one compute for Cov?

• Covariance Covariance (Cov) (Cov) – a measure of the general movement relationship between two variables. It is usually measured in terms of correlation coefficient and asset allocation


• The following table summarizes the annual re turns you would have made on two companies: – One, a satellite and data

equipment manufacturer, and – Two, the telecommunica tions

giant, from 200A to 200J.


Year ONE TWO Year ONE TWO

Year ONE TWO

200A200A 80.95 58.26 200E 200E 32.02 2.94 200I200I 11.67 48.64 200B200B -47.37 -33.79 200F200F 25.37 -4.29 200J 200J 36.19 23.55200C200C 31.00 29.88 200G200G -28.57 28.86 200D200D 132.4 30.35 200H 200H 0.00 -6.36

If the correlation of these two If the correlation of these two investments is 0.54069, estimate the investments is 0.54069, estimate the variance of a portfolio com posed, in variance of a portfolio com posed, in equal parts, of the two investments.equal parts, of the two investments.

ILLUSTRATIVE PROBLEM 1ILLUSTRATIVE PROBLEM 1

1.1. Expected or Average Stock Return Expected or Average Stock Return 2.2. Variance of Stock returns of each Variance of Stock returns of each 3.3. Standard Deviation of Stock returns Standard Deviation of Stock returns

of each of each

Demand for thecompany's products

Probability of thisdemand occurring

Rate of Return on stock if this demand occurs

Company 1 Company 2Strong 0.30 100% 20%Normal 0.40 15% 15%Weak 0.30 -70% 10%

1.00


4.4. Coefficient of Variation of eachCoefficient of Variation of each5.5. CovarianceCovariance6.6. Assuming that you are to invest 30% of your Assuming that you are to invest 30% of your

investment funds in Company 1 and 70% in investment funds in Company 1 and 70% in Company 2, and their Correlation is 0.351 Company 2, and their Correlation is 0.351 compute for the: (A)Variance of 2-Asset Portfolio compute for the: (A)Variance of 2-Asset Portfolio (B) Standard Deviation of the 2-Asset Portfolio(B) Standard Deviation of the 2-Asset Portfolio

Demand for thecompany's products

Probability of thisdemand occurring

Rate of Return on stock if this demand occurs

Company 1 Company 2Strong 0.30 100% 20%Normal 0.40 15% 15%Weak 0.30 -70% 10%

1.00


• SML: ki = kRF + (kM – kRF) β i

• Beta Estimate Beta Estimate ( (β) of an individual stock is the correlation between the volatility (price variation) of the stock market and the volatility of the price of the individual stock.

• The beta is the measure of the undiversifiable, systematic market risk.

The SML commonly adopts the CAPM model


• If β = 1.0, then the Asset is an average asset.

• If β > 1.0, then the Asset is riskier than average.

• If β < 1.0, then the Asset is less risky than average.

• Can beta be negative?

Most stocks have betas in the range of 0.5 to 1.5


• The Hamada equation below is used to compute for new beta shall there be changes in capital structure.

• β β uu= Current, levered β .

• [1 + {(1-tax rate)(Debt/Equity)}]•



• In December 200B, AAA’s stock had a beta of 0.95. The Treasury bill rate at that time was 5.8%. The firm had a debt outstanding of P1.7B and a market value of equity of P1.5B; the corporate marginal tax rate was 36%. The registered risk premium at December 200B is 8.5%.


ILLUSTRATIVE PROBLEM 2ILLUSTRATIVE PROBLEM 2• In December 200B, AAA’s stock had a beta of 0.95. The

Treasury bill rate at that time was 5.8%. The firm had a debt outstanding of P1.7B and a market value of equity of P1.5B; the corporate marginal tax rate was 36%. The registered risk premium at December 200B is 8.5%.

– Estimate the expected return on the stock.

– Assume that a decrease in risk-free rate occurs and is attributed to an improvement in inflation rates, but that by January of 200C, the inflation rate deteriorates or increases by 1.25%, compute for the required rate of return of a marginal investor.



– Assume that marginal investors become more risk-averse and thus require a change in the risk premium by 4%, what will be the effect on their required rate of return?

– The current beta is 0.95. This is assumed to be a levered beta since this has been registered even if there is outstanding debt of P1.7B. Compute for unlevered beta.



– How much of the risk measured by beta in “g” above can be attributed to (1) business risk, and (2) financial leverage risk?

ILLUSTRATIVE PROBLEM 3 ILLUSTRATIVE PROBLEM 3 – Assume that the treasury bill rate is 8%

and the stock’s risk premium is equal to 7%.

– 1.Use SML to calculate the required returns

Securities Expected Returns BetaA 17.4% 1.29B 13.8 0.68C 1.7 -0.86D 8.0 0.00E 15.0 1.00

ILLUSTRATIVE PROBLEM 3 ILLUSTRATIVE PROBLEM 3 – 2. Compare the required returns and

the expected returns, determine which securities are to be bought.

– 3. Calculate beta for a portfolio with 50% A Securities and C Securities

– 4. How much will be the required return on the A/C portfolio in number 3 above

Securities Expected Returns BetaA 17.4% 1.29B 13.8 0.68C 1.7 -0.86D 8.0 0.00E 15.0 1.00

ILLUSTRATIVE PROBLEM 4• PG which owns and operates grocery

stores across the Philippines, currently has P50 million in debt and P100M in equity outstanding. Its stock has a beta of 1.2. It is planning a leveraged buyout (LBO) , where it will increase its debt/equity ratio of 8. If the tax rate is 40%, what will the beta of the equity in the firm be after the LBO?

HOMEWORK 1

• Zuni-GAS is a regulated utility serving Northern Luzon. The following table lists the stock prices and dividends on U Corp from 200A to 200J.

HOMEWORK 1• Compute for the expected return

• Estimate the average annual return you would have made on your investment

• Estimate the standard deviation and vari ance in annual returns.

Year Price Dividends



200A200A 36.10 3.00 200E 200E 26.80 1.60 200I 24.25 1.60200B200B 33.60 3.00 200F200F 24.80 1.60 200J 35.60 1.60200C200C 37.80 3.00 200G200G 31.60 1.60200D200D 30.90 2.30 200H 200H 28.50 1.60

HOMEWORK 2• Assume you have all your wealth (P1

million) in vested in the PSE index fund, and you expect to earn an annual return of 12 percent with a standard deviation in returns of 25 per cent. Because you have become more risk averse, you decide to shift P200,000 from the PSEi fund to Treasury bills. The T bill rate is 5%. Estimate the expected return and standard deviation of your new portfolio

HOMEWORK 3• Novell which had a market value of equity of

P2 billion and a beta of 1.50, announced that it was acquiring WordPerfect, which had a market value of equity of P 1 billion, and a beta of 1.30. Neither firm had any debt in its financial structure at the time of the acquisition, and the corporate tax rate was 40%.

• Estimate the beta for Novell after the acquisition, assuming that the entire acquisition was financed with equity.

HOMEWORK 2• Novell which had a market value of equity of P2

billion and a beta of 1.50, announced that it was acquiring WordPerfect, which had a market value of equity of P 1 billion, and a beta of 1.30. Neither firm had any debt in its financial structure at the time of the acquisition, and the corporate tax rate was 40%.

• Assume that Novell had to borrow the P 1 billion to acquire WordPerfect, estimate the beta after the acquisition

risk and returns acc09 financial management part 2

Documents

measure risk

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mean value

measure of volatility

shareholder value

expected discounted

expected present value