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Quantitative Methods

Case Studies

A monte Carlo Case Study (20

Marks)

Laura,’ a 57 year old unmarried woman, earns around 68,000 dollars per year with expenditure of 37,500 dollars. She hit away

14,000 dollars each year and collected 330,000 dollars in her RRSP and TFSA, and also a rented apartment worth 250,000 dollars.

She has a iixed pension given by her employer, although it is not indicated to price rise, and Is entitled to get complete benefits of

Canada Pension Plan and Old Age Security, for retirement. She did not have a very competent portfolio: one fourth of cash is there,

and most of it was in contracted sector ETFs, single stocks and business bonds. Due to wrong entry of ETFs in the account,

unnecessary taxes were charged. Even before reconstructing Laura’s portfolio,”he had to make certain that it matched with.her

financial aims. Laura’s main aim was to ascertain if she could retire before the age of 65, maybe as early as 60, therefore she had to

know if her investments could produce enough flow of cash after she retires. Monte Carlo may show a top possibility of success with

the allotment of equity of 70% ot 80%. Through a risky questionnaire and art open interview, Justin Ill ‘ascertain that Laura was the

best person for a portfolio of 60% fixed income and 40% equities. . Through Monte Carlo software, Justin entered the current

portfolio . size of Laura, her rate of savings, projected retirement expenditure, and other employer income and government pensions.

If Laura feels that working till the age of 63 was unpleasant, she could go for the reproduction again and with different estimation.

Increasing her anticipated returns or bringing down the rate of inflation, is only a thought, therefore, she will have to make some

stronger decisions: she will have to making some more savings, or bring down her rate of planned expenses after retirement.

Amazingly, by bringing up the allotment to fixed salary could increase her opportunity to succeed: in spite of th returns being lower

than the equities, the volatility is also less, which lessens the risk of helpless decline in the early years. At last, Laura decided to work

for 6 more years and plan her retirement at the age of 63. After this, Justin decided to help her make a fresh ETF portfolio to match

that goal: it was finalized at 30% short term business bonds, 30% GICs, and the rest of it was divided among Canadian, L’S and

global equities. Laura was able to make a notified decision through the Monte Carlo simulation, but this wasn’t the end of the

procedure. In two or three years time, she will have to visit the location again to see that she is still on the right path of her retirement

goal, as many issues like, loss of job, a legacy, new connections, increase in the interest rates, all these could bring a change in the

main suppusitions 1 ; and she will have to redo her plans. The possibilities are different before the age of 63. For each added year

that Laura works, her portfolio will addition instead of a decrease and this will lead to a thrilling difference: the success rate will rise

up by 25% points if she continues to work till the age of 61 instead of 60.

Answer the following question.

Q1. How much was Laura earning at the age of 57? (Hint: 68,000 dollars per year)

CASE STUDY (20

Marks)

The cost of fuel in running of an engine is proportional to the square of the speed and is Rs 48 per hour for speed of 16 kilometers

per hour. Other expenses amount to Rs 300 per hour. What is the most economical speed?

Answer the following question.

Q1. What is most economical speed?

6/6/2019 ISTM

2/2

Q2. What is a chi-square test?

Q3. What is sampling and what are its uses.

Q4. Is there any alternative formula to find the value of Chi-square?

Finoplastika Industries Ltd, Nigeria (20

Marks)

Time series analysis has two important aims: 1) recognizing the quality of the phenomenon shown by the series of studies, and 2)

Both the aims need the plan of the viewed time series data is recognized and somewhat officially explained: A time series is said to

be a ‘collection of observations made in sequence with time’. For example: recording level of daily rainfall, periodical total domestic

product of US, and monthly strength of the. workers in Marine Corps for a specific rank and MOS. The evaluation of time series

gives instruments for picking a symbolic model and delivering forecasts. There are two sorts of times series data: • Continuous: in

this the data consists of study at every moment, for example, seismic movement recorded on a seismogram. • Discrete: the data

contains recordings taken at different periods ,like, statistics of each month crime. Until the data is absolutely haphazard, studies in

time series are usually related to each and the following studies could be partly ascertain by the last values. For instance, the reasons

pertaining to the meteorology which have an effect on the temperature for any given day tend to have some affect on the next day’s

climate. Hence, the observations of the past temperature are helpful for predicting temperatures for the following days. • A time

series can be deterministic if there are no haphazard or feasible features but goes in a set and foreseeable manner. The data gathered

during the classical physics experiment like showing Newton’s Law of Motion, is one example of a deterministic time series. The

stochastic type of series is more appropriate to the econometric function. Stochastic variables contain undefined or arbitrary

viewpoint. Though the worth of each study cannot be precisely foreseen, calculating the various observations could follow the

expected method. These methods can be explained through the statistical models. According to these models, studies differ

erratically on the underlying mean value whtch is the role of time. Time series data can be put in the following categories: one or

more performance factors; trend, seasonality, cyclical function and random sound. Various kinds of time series predicting models

give forecasts through extrapolating the previous performance of the values of a specified \’l!riable of interest. Consecutive study in

econometric times series are generally not free and forecast can be made on the basis of last observations. Although precise

predictions can be made with deterministic time series, predictions of stochastic time series are restricted to ‘conditional statements

regarding the future on the basis of particular hypothesis.’ Armstrong (2001) says, “The basic Assumption is that the variable ui!!

continue in the future as it has behaved in the past. ” Particularly, the time series predictions are suitable for stochastic type of data in

which the fundamental root cause of variation like, trend, cyclical performance, seasonality, and uneven variations, do not change

radically m time. Therefore, modeling is considered to be more suitable temporarily instead of permanent predictions.

Answer the following question.

Q1.

Write briefly on time-series analysis. (Hint: recognizing the quality of the phenomenon shown by the series of

studies, and, both the aims need the plan of the viewed time series data is recognized and somewhat officially

explained)

CASE STUDY (20

Marks)

The bulbs manufactured by a company gave a mean life of 3000 hours with standard deviation of 400 hours. If a bulb is selected at

random, what is the probability it will have a mean life less than 2000 hours?

Answer the following question.

Q1. Calculate the probability.

Q2. In what situation does one need probability theory?

Q3. Define the concept of sample space, sample points and events in context of probability theory.

Q4. What is the difference between objective and subjective probability?