Q.687 Financial Markets and Products

Fahim Zakaria, a fund manager based in Qatar, manages a sovereign fund for the Qatari government. The fund has more than $12.6 billion in assets under management. The fund invests only in the shares of blue-chip firms and the sovereign bonds/bills of different countries. If the manager wants to include a 164-days U.S. Treasury bill which is quoted as 9, then determine the cash price of the bill. A $96 B $95.9 C $93.7 D $91 The correct answer is: B The cash price of the bill can be calculated with the following formula: Discount = (No. of days to maturity / 360 days) * Quoted priceDiscount = (164/360) * 9 = $4.1Cash price = Face Value – Discount = $95.9 *User Question: Kindly explain why did we find discount here. Did not understood the question.

FRM Part 1

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Q.210 Bonds

An investor pays $10,500 for a $10,000 nominal of a newly issued 5-year fixed interest bond which is redeemable at par. The bond pays a coupon rate of 8% half-yearly in arrears. Calculate the yield rate obtained by the investor. A 6.80% B 9.97% C 7.85% D 8.23% E 9.56% We know that, $$P=Fr × a_{\overline{n|}}+Rv^{n}$$ Then, $$10500=10000\times\frac{0.08}{2}\ a_{\overline{10|}}+10000v^{10}$$ Using a financial calculator, with N=10, PV= -10,500, PMT=400 and FV=10,000 then hit CPT then I/Y. Note that your calculator should be END mode with P/Y=1 and C/Y=1. The semi-annual yield rate is: $$i=3.4018\%$$ And thus the annual rate is: $$3.4018\%\times 2=6.8036\approx 6.80\%$$ *User Question: 8% half-yearly ?

Actuarial - FM(Financial Mathematics)

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Q.3230 Liquidity and Treasury Risk Measurement and Management

Abraham Maslow is an equity strategist at FinteeseCapital. He intends to use leverage to increase the returns on a convertible arbitrage strategy. The expected return on assets of the strategy is 11%. The fund has $16 million invested in the strategy and will finance the investment with 60% borrowed funds. The cost of borrowing is 7%. Using this information, the return on equity (\(ROE\)) is closest to: A 17% B 13.66% C 10.66% D 11% The correct answer is: A \(Debt=$16\times 0.60=$9.6\quad million\) \(Leverage\quad ratio={ total\quad assets }/{ equity }\) leverage ratio = \(Leverage\quad ratio={ 16 }/\left( 16-9.6 \right) =2.5\quad times\) \({ r }^{ e }=L{ r }^{ a }-\left( L-1 \right) { r }^{ d }\) Where: \({ r }^{ a }\) = return on assets \({ r }^{ e }\) = return on equity \({ r }^{ d }\)= cost of debt \(L\) = leverage ratio \( Return\quad on\quad equity=2.5\ast 11\%-\left[ \left( 2.5-1 \right) \left( 7\% \right) \right] =27.5\%-10.5\%=17\% \) *User Question: Debt is 60%, so Equity is 40%. L=1+60/40 = 2.5 RoE = 2.5*11-1.5*7

FRM Part 2

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Q.3892 Understanding Fixed-Income Risk and Return

An investor holds a $5 million (par value) in a 4.5% bond maturing on March 31, 2020. The bond is currently priced at 97.250 per 100 of par value to yield 5.250% on an annual basis for settlement on 30 June 2019. The total market value including accrued interest is $4,980,000. If the bond’s annual Macaulay duration is 2.500, then its dollar duration is closest to: A 237 B 462 C 231 The correct answer is: C). Dollar duration is the name given to money duration in the United States. $$ \begin{align*} \text{MoneyDur} &=\text{ AnnModDur} \times {\rm PV}^\text{Full}\\ &=\frac{\text{MacDur}}{1+y} \times {\rm PV}^{\text{Full}} \\ &=\frac{2.5}{1+0.0525}\times $97.2\approx $231 \end{align*} $$ *User Question: Hi, can someone explain the PVfull=97.2. I mean isn’t that number the clean price without taking into account the accrued interest with 91 days (April/30+May/31+June/30) into the settlement ?

CFA Level 1

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Q.34 The Time Value of Money

You have a choice to take your retirement benefit either as a lump-sum or as an annuity. You can take a lump-sum of $4.5 million or an annuity with 15 payments of $400,000 a year with the first payment starting today. The interest rate is 7% per year compounded annually. Which option is preferable, on the basis that it has the greater present value? A The lump-sum B The annuity C There's no difference between the two options The correct answer is: A). The first option's PV is 4,500,000. The second option is an annuity due with 15 payments, which means an immediate $400,000 at time t=0 plus an ordinary annuity of 400,000 per year for 14 years. PV of the second option is: PV=400,000+A*((1-1/(1+r)N)/r)=3,898,187.2, where A=400,000 N=14 r=7%=0.07. 3,898,187 Using the financial calculator: Annuity option: First, set the calculator to BGN by pressing 2ND PMT then 2ND ENTER then 2ND CPT (because the payments start today), then proceed as follows; N= 15; I/Y= 7; PMT=400,000; PV = 0; CPT => FV = 3,898,187.19 B is incorrect because the present value of the lump sum is greater than the present value of the annuity payments. C is incorrect because the present value of the lump sum is greater than the present value of the annuity payments. *User Question: It should be FV=0, CPT==>PV not FV

CFA Level 1

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Q.4620 Valuation and Risk Models

The futures price of an asset is USD 40, and the annual volatility of the futures price is 20%. If the risk-free rate is 5%, what is the value of a put option to sell futures in 6 months for USD 45? A USD 0.028 B USD 4.498 C USD 0.026 D USD 5.520 The correct answer is: D In this case, \({\text{F}}_{0}\)=40, K=45, r=0.05, s=0.20, T=0.5 The following formula gives the value of the put option: $$ { \text{P} }_{ 0 }=\text{K}{ \text{e} }^{ -{ \text{r} }\text{T} }\times \text{N}\left( -{ { \text{d} } }_{ 2 } \right) -{ \text{S} }_{ 0 }{ \text{e} }^{ -{ \text{r} }\text{T} }\times \text{N}\left( -{ { \text{d} } }_{ 1 } \right) $$ Where: \({\text{P}}_{0}\)= value of the put option \({\text{F}}_{0}\)= current futures price K= strike price s= volatility of the futures price r= risk-free rate T= time $$ { \text{d} }_{ 1 }=\cfrac { \text{ln}\left( \cfrac { { \text{F} }_{ 0 } }{ \text{K} } \right) +\cfrac { { \sigma }^{ 2 }\text{T} }{ 2 } }{ \sigma \sqrt { \text{T} } } =\cfrac {\text{ln}\cfrac { 40 }{ 45 } + \cfrac{{ 0.20 }^{ 2 }}{2}\times 0.5 }{ 0.20\sqrt { 0.5 } } =-0.76214 \\ { \text{d} }_{ 2 }={ \text{d} }_{ 1 }-{ \sigma \sqrt { \text{T} } }=-0.9036 \\ \text{N}\left( -{ \text{d} }_{ 1 } \right) =\text{N}\left( 0.762 \right) =0.7764 \\ \text{N}\left( -{ \text{d} }_{ 2 } \right) =\text{N}\left( 0.9036 \right) =0.8159 $$ The value of the put option is given by: $$ { \text{P} }_{ 0 }=\text{K}{ \text{e} }^{ -{ \text{r} }\text{T} }\times \text{N}\left( -{ { \text{d} } }_{ 2 } \right) -{ \text{S} }_{ 0 }{ \text{e} }^{ -{ \text{r} }\text{T} }\times \text{N}\left( -{ { \text{d} } }_{ 1 } \right) \\ { P }_{ 0 }=45{ \text{e} }^{ -0.05\times 0.5 }\times 0.8159 -40{ \text{e} }^{ -0.05\times 0.5 }\times 0.7764=\text{ USD } 5.520 $$ *User Question: I do not understand why the calculation of d1 does not take into account the risk free rate. Any thoughts as to why that is the case? My d1 = -0.5856 .

Q.378 Quantitative Analysis

A random sample of 50 FRM exam candidates was found to have an average IQ of 125. The standard deviation among candidates is known (approximately 20). Assuming that IQs follow a normal distribution, carry out a statistical test (5% significance level) to determine whether the average IQ of FRM candidates is greater than 120. Compute the test statistic and give a conclusion. A Test statistic: 1.768; Reject H0 B Test statistic: 2.828; Reject H0 C Test statistic: 1.768; Fail to reject H0 D Test statistic: 1.0606; Fail to reject H0 The correct answer is: A The first step: Formulate H0 and H1H0: μ = 120H1:μ > 120Note that this is a one-sided test because H1 explores a change in one direction onlyUnder H0, (x̄ - 120)/(σ/√n) ∿N(0,1) Next, compute the test statistic: = (125 – 120)/(20/√50) = 1.768Next, we can confirm that P(Z > 1.6449) = 0.05, which means our critical value is the upper 5% point of the normal distribution i.e. 1.6449. Since 1.768 is greater than 1.6449, it lies in the rejection region. As such, we have sufficient evidence to reject H0 and conclude that the average IQ of FRM candidates is indeed greater than 120. Alternatively, we could go the “p-value way” P(Z > 1.768) = 1 – P(Z < 1.768) = 1 – 0.96147 = 0.03853 or 3.853%This probability is less than 5% meaning that we have sufficient evidence against H0. This approach leads to a similar conclusion. *User Question: Can you please explain how did we get P(Z > 1.6449) = 0.05 ?

Q.4666 Valuation and Risk Models

The standard deviation of the daily portfolio value changes is given as 0.0231, and its mean as 0.0012. Given that there are 250 trading days in a year, what is the annual 99% VaR for the portfolio according to the delta-normal model? A 0.78 B 0.83 C 0.58 D 0.63 The correct answer is: B According to delta-normal mode, VaR is given by: $$ \text{VaR}={ \mu }_{ \text{P} }+{ \sigma }_{ \text{P} } { \text{U} } $$ Since we are dealing with 99% VaR, it implies that $$ \text{U}=-2.326 $$ So that daily VaR is given by: $$ \begin{align*} \text{VaR}=& 0.0012+0.0231\times-2.326=-0.05253 \\ \text{Annual VaR}=& \sqrt{250}\times-0.05253=-0.8306 \end{align*} $$ *User Question: While scaling up and finding an annual VAR, shouldn't the return be multiplied by 250 and the standard deviation be multiplied by square root of 250. Since we will use the property that the sum of 'n' IID with mean R and Std Dev D is n*R and (square root of n)*(Std Dev D). This will give us a normal distribution with mean of n*R and std dev of (square root of n*Std Dev D), which will be 250*0.0012= 0.3 (mean) and standard deviation of (square root of 250)*0.0231= 0.3652. Now applying U = -2.33 we get VAR as 0.5509. How can we scale up a value of a normal distribution at a particular percentile directly by the square root of time as it is done in the solution?

Q.528 Quantitative Analysis

An autoregressive process is considered stationary if: A The roots of the characteristic equation lie on the unit circle B The roots of the characteristic equation lie outside the unit circle C The roots of the characteristic equation lie inside the unit circle D The characteristic equation are of order 1 The correct answer is: B In any autoregressive process, the roots of the characteristic equation must lie outside the unit circle, which means the absolute value of the roots must be larger than one. *User Question: which roots and unit circle are these? what do they imply. ?

Q.3190 Risk Management and Investment Management

Jack Marconi is an equity strategist at Gandhara Investment and is evaluating the performance of four large-cap equity portfolios: Azgard, Lambda, Tricky, and Jackpot. As part of his analysis, Jack computes the Sharpe ratio and the Treynor measure for all four funds. Based on his finding, the ranks assigned to the four funds are as follows: $$ \begin{array}{|c|c|c|} \hline Fund & Treynor\quad Measure\quad Rank & Sharpe\quad Ratio\quad Rank \\ \hline Azgard & 1 & 4 \\ \hline Lambda & 2 & 3 \\ \hline Tricky & 3 & 2 \\ \hline Jackpot & 4 & 1 \\ \hline \end{array} $$ The difference in rankings for Funds Azgard and Jackpot is most likely due to: A Different benchmarks used to evaluate each fund's performance B A difference in risk premiums C A lack of diversification in Azgard Fund as compared to Jackpot Fund D None of the above The correct answer is: C The most likely reason for a difference in ranking is due to the absence of diversification in Azgard Fund. The Sharpe ratio measures excess return per unit of total risk, while the Treynor ratio measures excess return per unit of systematic risk. Since Azgard Fund performed well on the Treynor measure and so poorly on the Sharpe measure, it seems that the fund carries a greater amount of unsystematic risk, meaning it is not well diversified and unsystematic risk is not the relevant risk measure. *User Question: Hello, I believe the explanation is not correct (the answer is correct though). Azgard is the fund that performed poorly on the TREYNOR ratio and performed well on the Sharpe (not vice versa as you state it) Therefore, Azgard carries a greater amount of systematic risk (Beta is greater ,therefore Traenor is low) or it was not well diversified. Please comment because the current explanation is confusing - e.g. if a porftolio performes well on the Treynor it means it is WELL diversified.