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Study Session 2: Quantitative Methods: Basic Concepts

Probability concept problem-session 2 Challenge problems 4.b & c

Hi all,

I have a question regarding the probability concept. Please help. Thank you very much.

Below is the question in Probability concept problem-session 2 Challenge problems 4.b & c

A bond that matures in one year is priced at $950 today. You estimate that it has a 10% probability of default. If the bond defaults, you expect to recover $600. If it does not default, it will pay $1080 at maturity. The nominal 1-year risk-free rate is 7.5%

B. What is the expected payoff on the bond in one year?

Answer is 0.1(600) +0.9(1080)=1032

Annualizing YTM

I have a quick question about the need to annualize YTM rates.  This question came about initially after looking at FINRA’s TRACE system to see how YTM is quoted in practice.  The bond I looked at was HD.GK and bought on the first day of availability for 99.248 with a coupon rate of 5.875 compounded semi-annually for 30 years.  When I used Excel to calculate the YTM I got exactly half of the YTM listed in the system (5.929) and so I had to multiply it by 2 to reannualize it.  It took me a bit to be “convinced” of all of this but it led to two questions:

Time Weighted return and dividend reinvestment

Hi everyone,

When using the time weighted return method, would a dividend reinvestment affect the second year period beginning balance? For example, if a t=0 I purchase a stock at $100, at the end of the year I get a $2 dividend and purchase another stock for $105. At the end of year 2, I sell both stock for $110 and get $2 per stock.

Time weighted return without reinvestment = 6.83%

105 + 2 -100/100 = 7%

220 + 4 - 210/ 210 = 6.67%

(1.07 * 1.0667)^0.5 = 6.83%

Time weighted return with reinvestment: 6.33%

105 + 2 -100/100 = 7%

Simple Standard Deviation of Returns

Hi all,

I know this isnt 100% (no pun intended), but I just want to make sure I am atleast looking at these numbers somewhat correctly.

If you wanted to determine the probability of returns for a portfolio using the expected return, standard deviation of returns and R Squared would it simply be

Expected return +/- 1STD = 68% probability

Expected return +/- 2STD = 95% probability

Expected return +/- 3STD = 99.7% probability

Time weighted vs money weighted rate of returns

Hi guys,

If someone actually has control over the deposit and withdrawals in an investment account, would the money weighted rate of return be more appropriate than the time weighted rate of return? In this case, why couldn’t we still use the time weighted rate of return?

thanks for your help!

Trouble calc'ing exponents

I’m having a rough time accurately calculating exponents. I’m using BA2 Plus. I understand the yX button for exponents. I understand order of operations. WolframAlpha shows accurate answer so it’s not a mistake. Can’t figure out how to get $500,000. See example below.

The answer is $500,000.

Holding Period Return Question

Hi,

The answer below shows the return for the first holding period as 60% which assumes P1 (ending value) as $75. Shouldn’t P1 = $100 since “she sells both shares for $100 each.”?

Thanks for in advance for helping me understand this.

-j

Assume an investor makes the following investments:

Geometric mean vs. CAGR

This is Challenge Problem 1C from Schweser’s ”Structural Concepts and Market Returns” section in Study Session 2.

———-

Table

Year  /  Year-End Share Price  /  Year-End Dividend  /  Holding Period Return

Annuity Due / Time Value of Money - Schweser Challenge Problem #1 - Solution Error?

“The Parks plan to take three cruises, one each year. They will take their first cruise 9 years from today, the second cruise one year after that, and the third cruise 11 years from today. The type of cruise they will take currently costs $5,000, but they expect inflation will increase this cost by 3.5% per year on average. They will contribute to an account to save for these cruises that will earn 8% per year. What equal contributions must they make today and every year until their first cruise (ten contributions) in order to have saved enough at that time for all three cruises?