CFA Level 1 (2009) - 1

Study Session 3

Cross-Reference to eFA Institute Assigned Reading #12 - Technical Analysis

ANSWERS - CONCEPT CHECKERS

I.B Technical analysis gives signals when to buy, and incorporates psychological and economic reasons for price changes. Technical analysis does not have any explanawry power-it does not give a reason why investors are buying or selling.

2.e Technical analysis does require subjective judgment to interpret its rules. It has not been

shown to outperform fundamental analysis. Technical analysis relies on price patterns and does not incorporate accounting data.

3.B When the majority of people are negative, as the sentiment index indicates, contraryopinion technicians take the opposite opinion and will be bullish and buy.

4.B The aTe market is more speculative than the NYSE market. When people are buying more speculative issues. the majority of people are bullish. Contrary-opinion technicians will take the opposite stance-they will be bearish and sell.

.:; A In pt:riods of confidence. investors _,ell higher-quality bonds and buy lower-qualirv bOlld, looking for )·icld. Thi.' happens when til<: confidence index rises or whe'll spread, 11;11"1"(\\\

(1. B When investors are pessimistic. the confidence index Ellis.

RWhen margin debt balances in brokerage accounts increase. smarr money technicians will see this as a bullish sign thal investors arc bl1\·jng. Contrary-opinion techniciam will take the opposite stance and will be bearish.

8.A Technicians believe that srock prices move in trends, that history does tend to repeat itself, and that prices react slowly to new information.

'). A A smarr money technician will follow the behavior of other investors. Bullish signs would be increases in the confidence index, a narrowing of the T-bill Eurodollar spread, and increases in brokerage account debit balances.

10.B If the relative strength ratio (stock price/market index value) increases, the percentage increase in the stock price must be greater than the percentage increase in the market index value.

I I. e A smarr money technician will follow the behavior of other smarr inveswrs. Bearish signals would be a wider Tbill Eurodollar spread, a falling Barron's confidence index. and falling debit balances (margin debt) in brokerage accounts.

12. e A high put/call ratio indicates invesrors arc bearish, which would be a bullish indicator to a contranan.

SELF-TEST: QUANTITATIVE METHODS

1.Allan Jabber invested $400 at the beginning of each of the last 12 months in the shares of a mutual fund that paid no dividends. Which method will he correctly choose in order to calculate his average price per share from the monthly share prices?

A.Arithmetic mean.

B.Harmonic mean. C. Geometric mean.

2.The central limit theorem and Chebyshev's inequality apply to which

3.Colonia has onh rwo political parties, the \\ligs and the \\/ags. If tht· W'ags are

currenr polls, thtre is a 20% probability that the \X!ags will be elected. The sum of the (unconditional\ probability of a tax increase and the joinr probability that the Wigs will be elected and there will be no tax increase arc rlosest to:

A.55%.

B, 70%,

C.85%.

4.Analysts at Wellborn Advisors are considering two well-diversified portfolios based on firm forecasrs of their expected returns and variance of returns. James argues that Portfolio 1 will be preferred by the client because it has a lower coefficienr of variation. Samantha argues thar Portfolio 2 would be preferred by the client because it has a higher Sharpe ratio. The client states that he wishes ro minimize the probability that his portfolio will produce returns less rhan the risk-free rarc. Based on this information, the client would most lil;:e{v prefer:

A.] 00% in Portfolio],

B.100% in Portfolio 2.

C.some combination of Portfolios 1 and 2.

5.Ralph will retire] 5 years from today and has saved $121,000 in his investment account for retiremenL He believes he will need $37,000 at the beginning of each year for 25 years of retirement with the first withdrawal on the day he retires. Ralph assumes that his investment account will rerum 8%. The amount he needs [0 deposit at the beginning of this year and each of the following 14 years (15 deposits in all) is closest to:

A.$1,350.

B.$1.450.

C.$1,550.

Self-Test: Quantitative Methods

6.The current price of Bosto shares is E50. Over the coming year, there is a 40% probability that share returns will be 10%, a 40% probability that share returns will be 12.5%, and a 20% probability that share returns will be 30%. Bosto's expected return and standard deviation of returns for the coming year are closest to:

7.Nikki Ali and Donald Ankard borrowed $15,000 to finance their wedding and reception. The fully-amortizing loan at 11 % requires equal payments at the end of each of the next seven years. The principal portion of the first payment is closest to:

A.$1,500.

B.$1,530.

C.$1,560.

8.\X!hich of the following statements about probability distributions is least accurate?

A.Continuous uniform distributions have cumulative distribution functions that are straight lines from zero to one.

B.The probability that a continuously distributed random variable will take on a specific value is always zero.

C.A normally distributed random variable divided by its standard deviation will follow a standard normal probability distribution.

9.Market technician Christine Collies uses the Barron's confidence index as a "smart money" indicator and uses the CBOE put-call ratio as a contrarian indicator. Given that both of these indicators have recently risen sharply, her

market outlook based on each indicator is most likely:

10.Given the following data:

•There is a 40% probability that the economy will be good next year and a 60% probability that it will be bad.

•If the economy is good, there is a 50% probability of a bull market, a 30%

probability of an average market, and a 20% probability of a bear market.

•If the economy is bad, there is a 20% probabiliry of a bull market, a 30% probability of an average market, and a 50% probability of a bear marker.

The unconditional probability of a bull market is closest to:

A.20%.

B.32%. C. 50%.

Self-Test: Quantitative Methods

11.x, Y, and Z are independently distributed. The probability of X is 30%, the

probability ofY is 40% and the probability of Z is 20%. Which of the following is closest to the probability that either X or Y will occur?

A.70%.

B.58%.

C.12%.

12.Which will be equal for a I-year T-bill with 360 days to maturity?

A.Bank discount yield and money market yield.

B.Money market yield and holding period yield.

C.Effective annual yield and bond equivalent yield.

13.The percentage changes in annual earnings for a company are approximately normally distributed with a mean of 5% and a standard deviation of 12%. The probability that the average change in earnings over the next five years will be greater than IS.5% is close.ft to:

A.2.5%.

B.o

5.0AI.

C.10.0%.

14.Which of the following is least like~]i correct concerning a random variable that is lognormally distributed?

A.It has a symmetric distribution.

B.The natural logarithms of the random variable are normally distributed.

C.It is a univariate distribution.

15.A discrete random variable x can take on the values 1,2, 3,4. or 5. The probability function is Prob(x) = x/15, so the cumulative distribution function is

t(~). The cumulative probability, F(4), and P(2 < x :s 5) are:

Self-Test: Quantitative Methods

SELF-TEST ANSWERS: QUANTITATIVE METHODS

1. B The harmonic mean of the 12 purchase prices will be his average price paid per share.

2.C Both the central limit theorem and Chebyshev's inequality apply to any distribution.

3.C The unconditional probability of a tax increase is: 0.2(0.32) + 0.8(0.6) = 54.4%.

The joint probability that the Wigs will be elected and there will be no tax increase is:

0.8(0.4) = 32%. The sum is: 54.4 + 32 = 86.4%.

4.B A portfolio that has a higher Sharpe ratio will have a lower probability of generating returns less than the risk free rate. With a target return equal to the risk-free rate the

ratio for a portfolio is (E[RpJ - Rf) / (fp'which is also the Sharpe ratio. Portlolio 2 will have a lower probability of returns less than the risk-free rate. Since both portfolill.\ are well divcrsified and Portfolio J has a lower Sharpe ratio than Portfolio 2, an:' allo('llioll !() Portfolio 1 would decrease the over'lll portfolio's Sh.lrpe alld s.d"ctv-f1rst ratios. increasing the probabilill of rClUrns Icss th'1I1 the risk-fret· ran:.

5.B Step 1: calculate the amount needed at retirement at t = 15. with calculator in BGN

Illode:

N = 2'). rV = O. Ill' = 8. PMT = 37.000, CPT PV = -426,564.

Step 2: Reduce this b:' the t = 15 value of current savings.

42G.'i64 - 121.000(l.08jl 'i= 42.732.

Step 3: calculate the required deposits at t = 0,1, .... ,14 to result in a time 15 value of 42,732, with calculator still in BGN mode,

PV = 0, N = 15, Ill' = 8, FV = 42.732, CPT PMT = -$1,457.22.

To check, in BGN mode. N = 15. I/Y = 8, PMT = 1.457.22, PV = 121,000,

CPT FV ~ -426,564.59.

6.A EIR] = (0.4)(10) + (0.4)(12.5) + (0.2)(30) = 15%.

Variance = (0.4)(10- 15)~ + (0.4)(12.5 - 1W + (0.2)(.')0 - 15)~ = 57.5.

Sm1dard deviation = .J57.'i = 7.58%.

7.B The inrereSI portion of the first paymenr is simply Principal x Interest rate = (15.000 x 0.11)=1,650

Using a financial calcularor: PY = 15,000, FV = 0, Ill' = 11, N=7, CPT PMT= $3,183.

Principal = Payment - Interest = 3,183 - 1,650 = 1,533.

8.C A standard normal probability distribution has a mean of zero, so subtracting the mean from a normal random variable before dividing by its standard deviation is necessary to produce a standard normal probability distribution.

Self-Test: Quantitative Methods

9.A An increase in the confidence index typically indicates that high-grade bond yields and average bond yields are moving closer together, a bullish indicator when used as a smart money indicator. An increase in the put-call ratio indicates that options traders are buying more puts than calls, which would be bullish when used as a contrary indicator.

10.B Using the total probability rule, the unconditional probability of a bull market is

0.50(0.40) + 0.20(0.60) = 32%.

11.B Probability of X or Y is P(X) + P(Y) - P(XY).

0.3+ 0.4 - (0.3)(0.4) = 58%.

12.B Since the money market yield is the holding period yield times #days/360,

HPY x 360/360 = HPY = MMY.

FORMULAS

nominal risk-free rate = real risk-free rarc + expected inflation rate

+default risk premium

+liquidity premium

+maturity risk premium

effecrive annual rate = (l + periodic rate)m - 1

continuous compounding: er - 1 = EAR

z=~

i=! Xi

Book 1 - Ethical and Profcssional Standards and Quantitativc Methods

Formulas

n

weightcd mean: Xw = L:wjX j

i=l

position of the observation at a given percentile,y: L, = (n +I)L

) 100

range = maximum value - minimum value

excess kurtosis = sample kurtosis - 3

n

L:IXj-XI

r - rf

Sharpe ratio = _r__

(JI'

joint probability: P(AB) = PtA I B) x p(B)

addition rule: PlA or H) = PtA) + p(B) - p(AB)

multiplication rule: PtA and B) = PtA) x PCB)

total probability rule: P(R) = P(R I SI) x p(Sj) + p(R I S) x P(S2) + , , , + plR I SN) x P(SN)

(n-x)l x !

for a bi nomial random variable: E(X) = nr

for J. 110rmal variable:

continuously compounded rate of return: rcc = In( ~J 1= In(1 + HPR) so;

sampling error of the mean = sample mean - population mean = x- 11.

a standard error of the sample mean: ax = J;;,

Book 1 - Ethical and Professional Standards and Quantitative Methods

Formulas

s standard deviation of the sample mean: Sx = ,J;;

confidence interval: point estimate ± (reliability factor x standard error)

confidence interval for the population mean: x± zo/2 ~