Investments
required rate of return (CAPM Formula)
CAPM formula: R = Rf + B * (Rm - Rf) Rf = Risk free rate B = Beta Rm = Market Rate (may already give the market premium vs having to calculate it)
Bond conversion formula
Conversion value = (Par value/conversion price) * stock price
Duration has an inverse relationship to what?
INterst rates are INverse
Net Operating Income (NOI)
Income projected - Vacancy - Operating expenses (Not Mortgage) + Interest expenses = NOI / CAP rate = price to pay for property
Bond A has a 6% annual coupon and is due in 2 years. Its value in today's market is $900. Bond B has a 10% annual coupon and is due in 4 years. It is priced to yield 12%. Bond C is a zero-coupon bond priced to yield 11% in 8 years. Assuming the duration of Bond A is 1.94 years, which of the following statements about the effect of a 1% decline in interest rates is true? A) Bond C, having a longer duration that Bond A, would have a larger percent increase in price than Bond A. B) The percent change in price of a bond is independent of the duration of a bond. C) It is NOT possible to determine the percent change in price of Bond A versus Bond C because the duration of Bond C is NOT given. D) Bond A would have a greater percent change in price than Bond C because it has a shorter duration.
Rationale The correct answer is "A." In this instance, there's no need to do any calculations. They're already (inherently) done. Because it gives the duration of Bond A (directly) and Bond C (indirectly as zero coupon bonds always have a duration equal to their maturity), the longer duration bond (Bond C) will have the greatest sensitivity to interest rate changes (because of the longer duration). Bond B is ignored simply because it's not found in the answers as a choice. Thus, answer A is correct. Answer B is not correct because the percent price change is dependent on duration. Answer C is not correct because duration is given (indirectly by giving the maturity and the fact it's a zero). Answer D is incorrect simply because it's not true of duration. If you choose to calculate: Multiply the change of rate by the duration to arrive at the percent change in price (see formula sheet for percent change formula). For each percent of change, multiply by the duration to arrive at the total percent change. Then calculate that percentage into a price change. **This may exceed the 1.5 minutes per question suggested on the exam.
The form of technical analysis that utilizes Advances and Declines (also known as Breadth of the Market) as an indicator is known as: A) Price Indicator. B) Volume Indicator. C) Market Indicator. D) Charting Indicator.
Rationale The correct answer is "A." Advances and declines deal with price. Volume indicates the number of shares traded. Market indicators deal with directions of the market and related averages. Charts are used as indicators and in some instances, do not use price but rather movements.
During the peak of the economic cycle, which of the following should one undertake? I. Sell debt instruments II. Begin allocations to cash positions III. Buy debt instruments IV. Sell gold and real assets A) I and II only. B) II and III only. C) III and IV only. D) I and IV only.
Rationale The correct answer is "A." At the peak of the cycle, as the economy has reached full steam, it is an excellent time to sell not buy fixed (and generally lower return) instruments. It is also an excellent time to begin appropriations to cash in preparation for opportunities that may arise. Since inflation is still on (and rising after the peak), it often proves to be a good time to acquire metals rather than sell them.
Which of the following reveals the relationship of a given security's movement relative to that of the market? A) Beta. B) Correlation coefficient. C) Covariance. D) Standard deviation.
Rationale The correct answer is "A." Correlation coefficient and covariance measure two stocks movements relative to one another. Standard deviation measures a security's performance relative to expectations of performance. Alpha reveals the level of over or underperformance of the security relative to market expectations.
Which of the following represent the minimum information needed to calculate the weighted average rate of return for a portfolio? I. Current market price of each security. II. Price paid for each security. III. Number of shares of each security. IV. Total portfolio value. V. Percent return of each security. A) I, III and V only. B) II, III and IV only. C) III, IV and V only. D) I, IV and V only.
Rationale The correct answer is "A." Current market price times number of shares gives the total value of each investment. These can be summed to calculate the total portfolio value. Then, the total value of each investment is divided by the total portfolio value and multiplied by the percent return of each security to calculate the weighted return. These weighted returns added together give the weighted average portfolio rate of return.
Which one of the following factors would be the strongest indication that interest rates might rise? A) Selling of dollar-denominated assets by foreign investors. B) Decreasing United States government deficits. C) Decreasing rates of inflation. D) Weak credit demand by the private sector of the United States economy.
Rationale The correct answer is "A." Foreigners selling dollar-denominated assets are preparing to take advantage of higher rates by increasing their liquidity. The rest signal a decrease in rates.
The optimum portfolio is said to occur at the point of tangency of which of the following two measures? A) Indifference curve and efficient frontier. B) Standard deviation and median expected return. C) Beta coefficient and portfolio data. D) Covariance and correlation coefficient.
Rationale The correct answer is "A." The Indifference Curve is the risk return trade-off which investors are willing to make, while the Efficient Frontier is the best possible returns that could be expected from all possible portfolios. At the point of tangency, one has attained the optimal portfolio.
John Risotto has a cash need at the end of nine years. Which of the following investments best meets this need and serves to immunize the portfolio initially? I. An 11-year maturity coupon bond. II. A 9-year maturity coupon Treasury note. III. A series of Treasury bills. A) I only. B) II and III only. C) II only. D) I and II only.
Rationale The correct answer is "A." The process of portfolio immunization entails not maturity of a security, but its duration. Duration is based on coupon rate. The larger the coupon payment, the shorter the duration. This being the case, a bond generally pays higher interest than a note, and a note pays higher than short-term Treasury bills. Given this information, one could reasonably expect a shorter duration (than time to maturity), while receiving better immunization from the bond.
Which of the following is NOT a premium factor that would be considered part of the nominal rate of interest? A) Economic premium. B) Default premium. C) Liquidity premium. D) Risk free rate of interest.
Rationale The correct answer is "A." There is no such thing as an economic premium. All of the other premiums added to the risk free rate equal the nominal (or stated) rate.
You are faced with several fixed income investment options. Which of these bonds has the greatest reinvestment rate risk? A) A U.S. Treasury bond with an 11.625% coupon, due in five years with a price of $1,225.39 and a yield to maturity of 6.3%. B) A U. S. Treasury strip bond (zero-coupon) due in five years with a price of $735.12 and a yield to maturity of 6.25%. C) A corporate B-rated bond with a 9.75% coupon, due in five years with a price of $1,038.18 and a yield to maturity of 8.79%. D) A corporate zero coupon bond due in 5 years with a price of $750 and a yield to maturity of 5.9%.
Rationale The correct answer is "A." This is due to the high coupon and lack of similar rates currently.
What is the portfolio deviation of a portfolio invested 60% in stock "A" with a 15% return and a deviation of 17.5%, and the balance in stock "B" with an 18% return and a 16.75% deviation. There is a .29 correlation between the two securities. A) 16.2% B) 14.0% C) 13.05% D) 4.69%
Rationale The correct answer is "B." COV = .175 x .1675 x .29 = .0085 s p = √(.60)2(.175)2 + (.40)2(.1675)2 + 2(.60)(.40)(.0085) s p = √.011 + .0045 + .0041 s p = √.0196 s p = .1399
An analysis of the monthly returns for the past year of a mutual fund portfolio consisting of two funds revealed the following statistics: Fund A total return = 18% Fund A Standard deviation = 23% Fund A Percentage of portfolio = 35% Fund B total return = 11% Fund B Standard deviation = 16% Fund B Percentage of portfolio = 65% The Correlation Coefficient ("R") between the two funds equals .25. What is the standard deviation of the portfolio? A) 13.16% B) 14.66% C) 18.45% D) 19.50%
Rationale The correct answer is "B." The information in [ ] is the COV formula. compute that prior to multiplying 2(.35)(.65)COVij s p = √(.35)2(.23)2 + (.65)2(.16)2 + 2(.35)(.65)[(.23)(.16)(.25)] s p = √.0065 + .0108 + .0042 s p = √.0215 s p = .1466
Match the investment characteristic(s) listed below which describe(s) closed-end investment companies. A) Passive management of the portfolios. B) Shares of the fund are normally traded in major secondary markets. C) Both "A" and "B." D) Neither "A" nor "B."
Rationale The correct answer is "B." Close-end funds are traded on the secondary markets but are not passively managed.
Your client holds a diversified equity portfolio, and has asked for your opinion on what is the most important factor to consider as he prepares to add additional equity securities. You tell him: A) Standard deviation of the new additions. B) Correlation of the new securities to the portfolio. C) Coefficient of variation of the new securities. D) Beta of the new securities to the existing portfolio.
Rationale The correct answer is "B." Correlation of securities is always the strongest determinant as to what should be added to a portfolio.
If the risk/return performance of a stock lies above the Security Market Line, the stock is said to have a: A) Positive correlation coefficient. B) Positive alpha. C) Positive expected return. D) Positive covariance.
Rationale The correct answer is "B." Performance of a stock below the SML is a negative alpha. Again, the Jensen formula can be used for this calculation.
The Federal Reserve Board is expected to sell large quantities of Treasury securities in the near future. What impact will these sales likely have on stock prices? A) Stock prices will decrease because the dividend growth rate of stocks will increase. B) Stock prices will decrease because the required rate of return for investors will increase. C) Stock prices will increase because interest rates will decrease as investors compete to purchase the Treasury securities. D) Stock prices will increase because the growth rate in dividends and earnings will increase.
Rationale The correct answer is "B." The sale of Treasury securities results in a reduction of cash in the market place, thus a decrease in supply causing an increase in demand. This will lead to an increase in the cost of money and a lessening of funds for investment, thus a reduction in stock prices.
The following set of newly issued debt instruments was purchased for a portfolio: - Treasury bond. - Zero-coupon bond. - Corporate bond. - Municipal bond. The respective maturities of these investments are approximately equivalent. Which one of the investments in the proceeding set would be subject to the greatest relative amount of price volatility if interest rates were to change quickly? A) Treasury bond. B) Zero-coupon bond. C) Corporate bond. D) Municipal bond.
Rationale The correct answer is "B." The smaller the coupon, the greater the volatility. Because the zero-coupon bond pays no payments, it is the smallest, thus the most volatile.
A bond fund had the following yearly returns: Year 1 at 14%, Year 2 at 7%, Year 3 at -3%, Year 4 at 18%, Year 5 at 9%. What is the standard deviation of the returns? A) 6.04 B) 7.13 C) 7.97 D) 8.43
Rationale The correct answer is "C." 12C 10Bii 14 ∑ + 14 ∑ + 7 ∑ + 7 ∑ + 3 CHS ∑ + 3 +/- ∑ + 18 ∑ + 18 ∑ + 9 ∑ + 9 ∑ + g Orange Shift s Sx,Sy
Specific companies are researched and chosen as investments based on their outstanding investment possibilities by analysts who practice: A) The Dow theory analysis. B) Top-down analysis. C) Bottom-up analysis. D) Random Walk analysis.
Rationale The correct answer is "C." Bottom up analysts are looking for the next big, but as yet, undiscovered stock that will break onto the scene. Bottom up analysts start with the company, then the industry and finally the economic climate. Top-down starts with the economic climate, moves to the industry and then the company.
Which one of the following statements correctly matches a technical indicator to the information it provides to signal a bear market? A) Odd lot theory indicates that the ratio of odd lot purchases to odd lot sales has been falling. B) Dow theory confirmation after the fact not predictive indicates that there is a decline in both the Dow Jones Industrial Average and Dow Jones Utility Average. C) A moving average chart indicates that actual prices have dropped through the moving 200 day average line. D) Barron's Confidence Index indicates that the yield differential between municipal bonds and corporate bonds is increasing.
Rationale The correct answer is "C." Choice "A" - Odd lot purchase levels indicate the number of small investors in the market. Odd lot theory says that small investors are always wrong. If odd lot purchases are falling relative to odd lot sales, it indicates the little guy thinks the market will fall. Since the little guy is always wrong, this would indicate a rally is coming, not a bear market. Choice "B" - The Dow Theory deals in three levels of market activity over time. Choice "D" - Barron's does not have a confidence index.
Which occurrence would potentially cause the greatest increase in a well-diversified common stock mutual fund? A) Unexpected inflation. B) Expected dividend increases. C) Unexpected corporate earnings growth. D) Expected increase in the prime interest rate.
Rationale The correct answer is "C." Choice "A" would have an adverse effect by dampening enthusiasm for new investments. Choice "B" would not cause "great increases." Choice "D" would dampen the activity.
Your client, Bill Brown, is an investor in ONLY dividend paying stocks. He buys them in time to catch the dividend and then sells them. You have a stock that you have researched, Gamma Globe, and it generally pays very high dividends relative to its price. What will you advise Bill to do in regard to this stock? A) Wait until the stock goes ex-dividend to make the purchase, and sell immediately thereafter. B) Get in on Gamma Globe's action for the long haul, that is "buy and hold." C) Purchase the stock to own it by record date, and sell when the price has rebounded. D) It doesn't matter when Bill buys it, but once purchased, Gamma Globe should be held only in preparation for almost certain subsequent price increases.
Rationale The correct answer is "C." It is the only answer that matches the client's express strategy. With the current T+2 settlement time frame, the client would need to purchase 2 business days prior to record date, or the business day prior to ex-date. Buy and hold is not what the client wants, and ex-dividend dates are too late to get in on the dividend action which the client seeks.
Assuming the current market yield for similar risk bonds is 8%, determine the discounted present value of a $1,000 bond with a 7.5% coupon rate which pays interest semi-annually and matures in 17.5 years. A) $504.68 B) $539.78 C) $953.34 D) $968.96
Rationale The correct answer is "C." N=17.5 x 2=35 i=8/2 = 4 PV=? PMT=(.075 x 1,000) / 2 = 37.50 FV= 1,000
As a measure for risk, the Capital Market Line (CML) uses the: A) Risk free rate of return. B) Beta of the market. C) Standard deviation of the market. D) Portfolio weighted beta.
Rationale The correct answer is "C." The CML (Capital Market Line) uses standard deviation, while the SML (Security Market Line) uses the beta as its "risk" measurement.
Of the following indexes, which is the only one that uses the geometric average to compute its daily value? A) NASDAQ Index. B) Wilshire 5000 Index. C) Value Line Average. D) Dow Jones Industrial Average.
Rationale The correct answer is "C." The NASDAQ, the NYSE Composite, and the Wilshire all use value weighted average, while the Dow Jones Industrial is a simple price weighted average. Only Value Line uses the geometric average.
Barbara Reed owns an LMN, Inc. bond with a par value of $1,000. LMN is a AA-rated bond that matures in 7 years. Barbara receives $55 of interest income from LMN semiannually. Comparable debt, i.e., is AA-rated, 7-year maturity, yields 12%. The bond's duration is 5 years. What is the intrinsic value of the bond? A) $703.36 B) $880.80 C) $953.53 D) $954.36
Rationale The correct answer is "C." The intrinsic value of a bond is its calculated present value. N = 7 x 2 i = 12 ÷ 2 PV = ? PMT = 55 ($110 ÷ 2) FV = 1,000
The value of the convertible bond as a debt instrument does not depend on which of the following? A) The bond's coupon. B) Current interest rates. C) The conversion price of the bond. D) The term of the bond.
Rationale The correct answer is "C." The value of the bond as a debt instrument is considered separately from its convertibility and is calculated using the bond formula or the present value methodology on the calculator. However, should the conversion value be greater than the "debt value" of the bond, it will sell for the higher price.
If the market risk premium were to increase, the value of common stock (everything else being equal) would: A) NOT change because this does NOT affect stock values. B) Increase in order to compensate the investor for increased risk. C) Increase due to higher risk-free rates. D) Decrease in order to compensate the investor for increased risk.
Rationale The correct answer is "D." A need for higher return to meet the onset of higher risk would drive the price of a security down (all other things being equal).
American Depository Receipts (ADRs) are for the following purpose(s): I. Finance foreign exports. II. Eliminate currency risk. III. Sell U.S. Securities in overseas markets. IV. Trade foreign securities in U.S. markets. A) I and III only. B) I and IV only. C) II and IV only. D) IV only.
Rationale The correct answer is "D." ADRs provide an opportunity for Americans to purchase foreign securities.
Using the following information, what is the duration of the bond being described? - Maturity is 11 years. - Par value is $1,000. - The coupon rate is 8.25%. - The bond is currently selling in the market at $1,094. - The bond pays interest annually. A) 12.4 years. B) 11 years. C) 9.3 years. D) 7.8 years.
Rationale The correct answer is "D." First the YTM must be calculated (7%). Once this is done, it can be plugged into the formula with the coupon rate and the number of periods, and reveals a Duration of 7.8 years. Step 1: Calculate YTM N = 11 i = ? PV = <1094> PMT = 82.50 FV = 1000 i = 6.9967 i = 7% Step 2: D = (1 + y) - (1 + y) + t (c - y) y c[(1 + y)t - 1] + y D = (1.07) - 1.07 + 11 (.0825 - .07) .07 .0825 [(1.07)11 - 1] + .07 D = 15.2857 - 1.2075 .1612 D = 7.7950
According to fundamental analysis, which phrase best defines the intrinsic value of a share of common stock? A) The par value of the common stock. B) The book value of the common stock. C) The liquidating value of the firm on a per share basis. D) The discounted value of all future dividends
Rationale The correct answer is "D." Intrinsic value is the discounted value of a future stream of cash flows. In the case of a stock, its dividends.
Which of the following is not an appropriate match? A) Classification by time: Spot markets. B) Classification by type of claim: Equity markets. C) Classification by participants: Mortgage markets. D) Classification by products: Money markets.
Rationale The correct answer is "D." Money market securities are short-term instruments categorized by time considerations, not product. Look at this from the product to determine the classification. For example, money markets and spot markets are classified as according timing because they are either short term maturities or current price. The common component when classifying these type of securities is timing. Equity and debt markets can be classified as to the order of claims in the event of liquidation. "Type of claims" simply refers to debt vs. equity and which is more senior. Bond markets, which include mortgage bonds, are divided into short, intermediate and long term markets. Each market has participants that prefer different segments of the yield curve. A participant in this case is an insurance company, bank, manufacturing company, etc. Different participants will prefer mortgage bonds over shorter term maturities.
Bond A has a 6% annual coupon and is due in 2 years. Its value in today's market is $900. Bond B has a 10% annual coupon and is due in 4 years. It is priced to yield 12%. Bond C is a 9% zero-coupon bond priced to yield 11% in 8 years. The yield to maturity of Bond A is closest to: A) 9.90% B) 10.45% C) 10.95% D) 11.91%
Rationale The correct answer is "D." N=2 i=? PV =<900> PMT=60 FV=1,000 Note: This is an annual bond so it's not necessary to adjust N, i or PMT.
Bob and Betty have approached you looking for the right hedge against possible, expected future inflation. You suggest to them that they: A) Invest in technology stocks. B) Invest in commodity futures. C) Invest in long-term U.S. Treasury issues. D) Invest in precious metals.
Rationale The correct answer is "D." None of the choices are necessarily stellar, but in contrast to the other choices, Option "D" makes far more sense, as metals have generally performed well as inflation hedges over time.
Of the pricing models we have examined, the following use "additional" factors to measure impact on return and arrive at appropriate portfolio returns: I. CAPM II. Black's Zero-Beta CAPM III. Merton's Multi-factor CAPM IV. Arbitrage Pricing Theory A) I only. B) I and II only. C) III only. D) III and IV only.
Rationale The correct answer is "D." Only Merton's Multi-factor CAPM and Ross' Arbitrage pricing theory include additional factors beyond standard rates found in the CAPM.
Lily Wassenbaum asks for your assistance in designing an educational investment program for her eight-year-old son, Max. She expects to need the funds in about 15 years when her AGI will be approximately $55,000. She wants to invest at least part of the funds in tax-exempt securities. Help her select which investment(s) would yield tax-exempt interest on her federal return if the proceeds were used to finance Max's education. I. Treasury bills. II. EE bonds. III. GNMA funds. IV. Zero coupon Treasury bonds. A) III and IV only. B) I, III and IV only. C) II and III only. D) II only.
Rationale The correct answer is "D." Options "I", "III" and "IV" all generate taxable income during their inclusion in Lily's portfolio: T-bills upon maturity, GNMA when income is paid, and Treasury zeros as the interest accrues within the bond, even though Lily will see no return paid to her. This is known as phantom income and it is fully taxable.
The duration of a bond is a function of its: I. Current price. II. Time to maturity. III. Yield to maturity. IV. Coupon rate. A) I and III only. B) II and III only. C) II and IV only. D) II, III and IV.
Rationale The correct answer is "D." The duration of a bond is not a function of the bond's price. Duration is used to estimate the price of a bond, given a change in interest rates.
What is the geometric rate of return for a stock that has experienced the following prices over a four-year period? Year 1 = $20 Year 2 = $32 Year 3 = $24 Year 4 = $28 A) 17.23% B) 15.78% C) 13.82% D) 11.88%
Rationale The correct answer is "D." There are many ways to solve this, but here is the quickest: N=3 i=? PV=<20> PMT=0 FV=28 Assume you paid $20 for the stock today and three years later, it is trading at $28.
Your client is considering the two stocks described below. Assume for this question that the risk-free rate is 6%, the expected return on the market is 14%, and the market's standard deviation is 18%. Stock A price per share = $18 Stock A annual dividend = $2 Stock A dividend growth rate = 3% Stock A Beta = 1.1 Stock A standard deviation = 21% Stock A realized return over past 12 months = 15% Stock B price per share = $12 Stock B annual dividend = $1.50 Stock B dividend growth rate = 4% Stock B beta = 0.88 Stock B standard deviation = 14% Stock B realized return over past 12 months = 12.5% Which stock would you recommend your client purchase, and why? A) Stock A, because its intrinsic value is greater than Stock B's. B) Stock A, because its required return is greater than Stock B's. C) Stock A, because its risk-adjusted return is greater than Stock B's. D) Stock B, because it is selling for less than its intrinsic value.
Rationale The correct answer is "D." Though there is a great deal of information here, one should be looking at the intrinsic values of the stocks and comparing them to the market prices of the stocks for over valuation or under valuation. A market selling price above intrinsic value is overvalued. A market price below the intrinsic value means the stock is undervalued and may be considered for purchase. The first step in this problem is to compute the required rate of return using the CAPM formula: R = Rf + B * (Rm - Rf) Stock A =14.8% = 6 + 1.1 * (14-6) Stock B = 13.04% = 6 + .88 * (14-6) Now that we have the required rate of return on the securities based on their volatility, I would utilize the Gordon Growth Model (or dividend model) to determine the price that the security should be at to be "fairly valued." V = D * (1 + g) / (R - g) Stock A =17.45 = [2 * (1+.03)] / (0.148-.03) Stock B = 17.25 = [1.5 * (1+.04)] / (0.1304-.04) So the "fair value" for our investor is $17.45 for stock A and it is trading at $18. Therefore the stock is overvalued (trading higher than its value). Stock B is valued at $17.25 for our investor and is trading at $12. Therefore the stock is undervalued (trading lower than its value).
Jim and Anne Taylor are baby boomers who would like to add an equity investment to their portfolio. They require a 12% rate of return and are considering the purchase of one of the following two common stocks: Stock 1: Dividends currently are $1.50 annually and are expected to increase 8% annually; market price = $35 Stock 2: Dividends currently are $2.25 annually and are expected to increase 7% annually; market price = $50 Using the dividend growth model, determine which stock would be more appropriate for the Taylors' to purchase at this time: A) Stock 2, because the stock is undervalued. B) Stock 2, because the return on investment is greater than the Taylor required rate of return. C) Stock 1, because its dividend growth rate is greater than Stock 2's growth rate. D) Stock 1, because the expected return on investment is greater than the Taylor required rate of return.
Rationale The correct answer is "D." Use the intrinsic value formula to determine whether the stock is over valued or under valued. Then use the expected rate of return formula to determine whether the stock meets the investor's required rate of return. r = D0(1 + g) + g (P) Stock 1 = $1.50 (1.08) + .08 = 12.63% $35 Stock 2 = $2.25 (1.07) + .07 = 11.82% $50
Unsystematic Risk (ABCDEFG)
Risk that can be diversified away Accounting Risk Business Risk Country Risk Default Risk Executive Rusk Financial Rusk Government/regulation Risk
Systematic Risk (PRIME)
Risk that can not be diversified away Purchasing Power risk Reinvestment Rate risk Interest Rate risk Market risk Exchange Rate risk
Duration equation
See CFP Sheet
IPS (TURRTLL)
Timeline unique circumstances reward risk taxes liquidity legal
Gordon Growth Model (Dividend Model)
V = D * (1 + g) / (R - g) V = Value D = Dividend g = Growth R = Required rate of return (CAPM)
R squared
determines the amount of return due to the market. If > 70% beta is a good measure of total risk, if less use STD = Correlation squared
Duration
is the weighted average maturity of all cash flows - the bigger the duration, the more price sensitive the bond is to interest rate changes - duration is the moment in time the investor is immunized from interest rate risk and reinvestment rate rusk - modified duration is a bond's price sensitivity to changes in interest rates - a bond portfolio should have a duration equal to the investors time horizon to be effectively immunized
Margin Call Formula
loan / 1- maintenance margin loan = share price x (1-inital margin)