The 36th Symposium, held at Saint Gallen University, Switzerland, from May 18 to May 20, 2006 was an extraordinary experience in my life. I met intellectually exceptional students and business leaders all over the world who have and will take part in changing our world to a better place to live.
Participating in the Symposium, I strongly felt that I have taken part in a special event that not only helped me think differently about the world but also encouraged me to do things for the benefits of both Europe and Asia. It was quite difficult to meet with 200 student participants and 600 business leaders but I have experienced open-mindedness and warm friendships of all participants. Coming to the Symposium, every one seized dialogues and new ideas and made friends with people from different cultures and backgrounds. I have learnt the most in the Symposium and I returned with enriched knowledge of future business potentials and an international network. I will never forget wonderful memories of Saint Gallen University, Zurich, Genève and agreeable moments with my Swiss friends.
I have never experienced such an excellent organization of the Symposium. Every thing was perfectly organized. I would like to thank much students, helpers and organizers who have contributed greatly to the success of the Symposium.
This year, 80% of speakers are CEO of international corporations such as Fiat, Degussa and Bayer. The speakers had excellent knowledge and experience in international leadership skills which leaders of today and leaders of tomorrow need to develop in order to contribute to the change of the world. I was touched by the presentation of Mr. Sergio Marchionne, CEO of Fiat. He said: “Leadership is a noble calling. It’s about enriching people’s live. It’s a sacred trust”. Discussed with Mr. Keiichiro Asao, a candidate for the position of Minister of foreign affaires of Japan this year, I learned that leadership in Japan needs more transparency. It’s also true in my home country, Vietnam.
In the Symposium, we discussed about topics of how to inspire Europe in the new economy. I really loved the discussions about how governments, civil society and global economy work together to strengthen Europe’s ability to thrive in the future and compete in the global marketplace. This is not only the question to Europe but also the question to Asia in the fast movement of the international capitalism. We also discussed about how to build a competitive society for sustained growth and development in the future. I had some truly good discussions with Japanese, Indian and American speakers from which I learnt that all today’s world-class leaders would like to encourage tomorrow’ leaders to change the world with brave business ideas and international leadership skills. I also shared my visions and business ideas with speakers and students and learnt from them the inspiration to work with international partners.
The 36th Symposium was a truly exceptional experience in my life. I have learned immensely and experienced an amazing time with participants. What I should say is that the Symposium is unique, incomparable and unforgettable.
Sunday, October 26, 2008
36th Symposium at St Gallen University (Switzerland)
In this essay, I regarded the whole world as a customer and a supplier, and entrepreneurship is beyond borders. Therefore, the new entrepreneurial formula to help entrepreneurs create viable businesses composes of 5 elements: Global Vision to know where to go in the future; Global Leadership Skills to lead their businesses in international environments; Technology Savvy to create new business and improve productivity; Multi-culture Awareness to shape company and customer cultures; and Entrepreneurial Passion to be successful in their venture of creating new global companies. These capabilities are essentially needed for entrepreneurs to transform their brave entrepreneurial ideas into flourishing global businesses.
To prepare for the 36th Symposium at St Gallen University in next coming May, I just attended an annual meeting of the St. Gallen Club of Japan held by the Swiss Embassy in Tokyo. I met with other 10 student-participants from Japan and the club members who shared wonderful experience in the past symposia. Currently, I am preparing questions and ideas about the topic “How to inspire and strengthen business relations between Europe and Asia” for special sections to discuss directly with the Symposium’s speakers. I intend to build a strong network with and introduce IUJ to the Symposium’s participants including students, politicians, scientists and business leaders. If you have any ideas or questions about those topics or the Symposium, please contact me so I can prepare to convey your ideas at this special international conference.
To prepare for the 36th Symposium at St Gallen University in next coming May, I just attended an annual meeting of the St. Gallen Club of Japan held by the Swiss Embassy in Tokyo. I met with other 10 student-participants from Japan and the club members who shared wonderful experience in the past symposia. Currently, I am preparing questions and ideas about the topic “How to inspire and strengthen business relations between Europe and Asia” for special sections to discuss directly with the Symposium’s speakers. I intend to build a strong network with and introduce IUJ to the Symposium’s participants including students, politicians, scientists and business leaders. If you have any ideas or questions about those topics or the Symposium, please contact me so I can prepare to convey your ideas at this special international conference.
Thursday, June 12, 2008
REPORT ON SMALL-GROWTH MUTUAL FUNDS
Introduction
Small Growth Mutual Funds’ objective is to maximize total return by investing in equity securities of small-growth companies in up-coming industries or young firms in their early growth stages. These funds are normally no-load, no-transaction fee funds investing in technology, health and service. Hence, they provide small investors with a reasonable alternative to direct purchase. Small investors can obtain good returns with the same degree of diversification of value-oriented stocks while avoiding heavy transaction costs.
In this report, we examine the performance of three small-growth funds: Value Line Emerging Opportunities (VLEOX), Turner Emerging Growth Fund (TMCGX) and JP Morgan Small Cap Growth Fund Sel (OGGFX). Then we will recommend the best fund that you should consider to invest in.
Fund Description
VLEOX is an open, medium-growth fund managed by Mr. Stephen E. Grant with the largest assets among the 3 funds (see table 01). TMCGX is a closed, small-growth, youngest and smallest fund managed by a team. OGGFX is an open, small-growth, team-managed and the oldest fund. TMCGX and OGGFX comply with the objective of investing primarily in stocks of small-growth companies in technology, health and service while VLEOX invests primarily in industrial cyclical. According to Morningstar’s rating, TMCGX is one among the top of 10% of the funds in the category since it was incepted. VLEOX and OGGFX are always among the next 22.5% of the fund in the category.
Fund Performance Analysis
Fund total return: According to the data provided by Morningstar, TMCGX had the nearly double quarterly and monthly total returns since inception date (see table 02) compared to the other 2 funds. For example, TMCGX’s total monthly return since inception date was 24.81% vs. 13.92% of VLEOX and 11.08% of OGGFX. OGGFX’s quarterly and monthly total returns since inception date were the lowest among 3 funds. However, there was no such big different among 3 funds in 5-year total returns. TMCGX seemed to have around 5% higher returns than the others.
Total return vs. benchmark: Table 03 represents the yearly total returns of 3 funds vs. Morningstar average category return, which is used as the consistent benchmark of return to compare the returns of 3 funds. Overall, 3 funds outperformed the market but VLEOX and OGGFX underperformed the market in 2003 while TMCGX still outperformed the market. In general, TMCGX always outperformed the market better than the other 2 funds in recent 5 years (see figure 01). This was illustrated by its higher returns compared to benchmark returns. Moreover, TMCGX’ performance to outperform the market was much more stable than the others. In other words, TMCGX’s performance has been consistent in excess return vs. benchmark.
Risk: As TMCGX had highest return, it seemed to have highest total risks among 3 funds. TMCGX’s standard deviation in 3 years is 15.24% vs. 14.52% (OGGFX) and 11.93% (VLEOX). Although 3 funds had higher Beta than market Beta, TMCGX had the highest Beta (1.59), then OGGFX with 1.49 and VLEOX with 1.21. The reason why VLEOX had the lowest total and nondiversifiable risks is that VLEOX is a medium-growth fund and it invests primarily in equity of medium-growth firms in industrial cyclical rather than investing in equity of young firms or firms in new industries that bear high risk.
Excess return:
VLEOX and OGGFX had negative Alpha (see table 04), which means that both of them underperformed the index (benchmark return) relative to how much volatility has been shown, or their actual returns are lower than their expected returns. On the other hand, TMCGX could achieve an actual return higher than its expected return by 1.31%. TMCGX also achieved greater return per unit of risk than the others (highest Sharpe ratio).
The excess return may due to selectivity rather than diversification. From table 05, we notice that VLEOX and OGGFX were more diversified than TMCGX in terms of numbers of stocks held but they had negative excess returns as discussed above. Moreover, they hold almost all domestic stocks and invest more than 90% of their fund capital in stocks (table 04). Meanwhile, TMCGX invested only 82.22% of its capital in stocks, kept 12.48% cash as a safe option and invested more than 2% in foreign stocks. Therefore, we see that the performance of small-growth mutual funds is not largely influenced by diversification but rather depends mainly on assets allocation and the choice of stocks in their portfolios. This means that the fund performance depends on fund management, which will be discussed later in this report.
Fund management:
We assess the management performance of each fund based on return from fund managers’ risk, which is return on the risk that fund managers take to manage fund assets. Given the desired non-diversifiable risk level at market Beta (beta=1), TMCGX had the largest return from manager’s risk 5.28% vs. 4.26% of OGGFX and 1.82% of VLEOX. Please see the table 06 for detailed calculation method. This means that TMCGX was best managed among 3 funds and OGGFX was well managed. Therefore, we see that fund performance depends largely on how well the fund is managed.
The 3 funds differ in their investment strategies. While TMCGX invests in diversified portfolios of companies that it believes have strong earnings prospects in emerging industries like health and technology, OGGFX invests in stocks of growth companies with leading competitive positions and seeks companies with predictable and durable business models capable of achieving sustainable growth. VLEOX focuses on companies that have expertise, theme or industry knowledge by stocks screening and fundamental analysis to identify companies that will provide super earnings. We see that the action of TMCGX is consistent with the stated objective of the small-growth fund but the actions of the other funds are not. As TMCGX seems to have the best performance, we are quite confident that it is better for investors to invest in a mutual fund that acts consistently with its objective.
Fund Prospect: VLEOX had the fastest growth rate of assets and largest fund size among 3 funds (see table 07). However, its performance in terms of total return was not better than the performance of TMCGX which is the smallest fund. This means that fund performance does not necessarily depend on the fund size and fund asset growth rate. Therefore, when making investment decisions, the investor should not look at the fund size and fund growth rate but rather examine the management quality of the fund under consideration.
Purchase and Expenses: OGGFX had the highest turnover rate (120%, table 04) but its performance was not the best. This is because this fund had higher transaction costs due to high turnover rate and fund performance is examined after all transaction costs. As a result, OGGFX appeared to perform worse than TMCGX due to more expensive transaction costs but not due to managers’ ability. Therefore, funds with low turnover rates seemed to outperform funds with high turnover rates. On the other hand, TMCGX has the largest expenses ratio so the fund might risk having poorer performance if its extra return is not sufficient enough to cover expenses.
Strengths and weaknesses of the funds: All three funds have ability to outperform the market and provide higher returns to the investor than the market return. They have good fund management and assets allocation to achieve differential return as well as low transaction expenses. However, all of them tend to volatile closely with market movement and bear high nondiversifiable risk. Please refer to table 08 for further details.
Conclusion
The overall performance of a mutual fund is not related to its size but depends on the fund’s investment objective, expenses ratio, turnover rates and especially the ability of fund managers. The ability to outperform the market of a fund relies more on the selectivity than on diversification of the fund’s portfolio.
There are some criteria for investment decisions in small-growth funds: investment objective, expenses ratio, turnover rates. More important criteria are the fund’s investment strategy, Alpha or excess return, fund management and asset allocation.
Based on our above analysis, we recommend that the investor should invest in TMCGX fund. However, OGGFX is a good alternative because this fund’s performance and management quality are very near to that of TMCGX.
Technique for Efficient Frontier Construction
Case 1: Short sale allowed with riskless lending & borrowing
- Purpose: to find tangent point A/tangency portfolio
- Technique: maximize the slope of the straight line RfA
- Find the weight of tangency portfolio
- Calculate expected return and standard deviation
- Plot the straight line RfA
Case 2: Short sale allowed with no riskless lending & borrowing
- Purpose: to find tangent point A/tangency portfolios at different risk free rate Rf to construct the frontier curve.
- Technique: find different tangent points at different Rf and plot the curve based on these tangent points
- Find the weight of tangency portfolio
- Calculate expected return and standard deviation
- Repeat these 2 steps when changing Rf by copying formula in Excel
- Plot the curve
Case 3: Short sale not allowed with riskless lending & borrowing
- Purpose: to find tangent point A/tangency portfolio
- Technique: maximize the slope of the straight line RfA
- Find the weight, expected return and standard deviation of tangency portfolio by using Solver with quadratic programming
- Plot the straight line RfA
Case 4: Short sale not allowed with no riskless lending & borrowing
- Purpose: to find tangent point A/tangency portfolios at different risk free rate Rf to construct the frontier curve.
- Technique: minimize the risk for any level of expected return to find different tangent points at different Rf and plot the curve based on these tangent points
- Find the weight of tangency portfolio, expected return and std by using Solver with quadratic programming
- Repeat this step when changing expected returns by writing a VBA program to repeat Solver
- Plot the curve
Portfolio Management – First Project
Benefits of diversification
From the Figure 01, we can see that the average risk of 1-stock portfolio is the largest (10.54%) and the risk of equally weighted 30-stock portfolio is the lowest (6.10%). These results reflect the concept of portfolio diversification: the risk of more diversified portfolio tends to be lower than the risks of less diversified portfolio. In a large diversified portfolio, the risk may reach to the average risk of a portfolio with a very large stock. As we can see from the shape of the curve, the risk of portfolio tends to decrease if the number of stock in portfolio increases. In other words, the more diversified portfolio has systematic risk (covariance) and has less unsystematic risk from individual stocks. However, when the number of stocks in portfolio is large enough, adding a more stock does not have a significant effect in reducing portfolio risk.
Portfolio Performance
The Figure 02 is a plot of risks and returns of equally weighted portfolios created in Part A and 8 30-stock portfolios of the weights WMVP1U, WMVP1C, WMVP2U WMVP2C, WOpt1U, WOpt1C, WOpt2U and WOpt2C in the 2nd half. From the graph that we can draw a line through the numbers of points plotted to present the relationship between risk and average return. The points above the line represent portfolio which have higher return than the points below the line given a risk level.
Choosing portfolios according to the objective
In this part, we will examine the choice of portfolio weights done by Solver on 30-stock portfolio for the 1st half and 2nd half data. The discussion will be based on the table of 30-stock portfolio.
For the purpose to minimize the risk of portfolio, we use Solver function to find the weights of a portfolio that has minimal risk or minimal variance. In the first half, in case of unconstraint, Solver tends to pick stocks of lowest average risks in a large portions to hold (e.g 10.61% of J:AJ@N(RI) with the lowest std. dev. of 6.89%, 25.39% of J:ASMR(RI) with the second lowest std. dev. 7.17%) and stocks with highest risks for short sales in a large portions (e.g -15.17% of J:IH@N(RI) of std. dev. 14.38%). In the 2nd half, in case of unconstraint, Solver suggests the largest weight of 38.63% of J:AJ@N(RI) with the lowest std. dev. (4.92%) and the largest weight for short sales at -21.45% of J:NK@N(RI) with the highest std. dev. 17.07%. In case of constraint, in both 1st and 2nd half, Solver also picks stocks with the lowest risks in large portions but is does not pick any stocks with negative weights for short sales due to the constraint that all the weights must be positive. The negative weights in case of unconstraint become zero in case of constraint. The largest positive weights in case on unconstraint remain the largest weights in case of constraint because those weights have minimal risks. This suggests that largest weights chosen by Solver are consistent with the objective of minimizing portfolio risks and some stocks are weighted more heavily because they have lower risks among available stocks in the portfolio. However, Solver does not pick stocks by choosing from the lowest risk stock to the higher risk stocks. For light weights, Solver tends to choose stocks with higher returns.
For the purpose to maximize the sharpe ratio, we use Solver function to find the weights of a portfolio that has maximal sharpe ratio or the maximal return on portfolio. In the first half, in case of unconstraint, Solver tends to pick stocks of highest average return in the heaviest weights (e.g 103.06% of J:SG@N(RI) with the highest return 3.36%). In the 2nd half, in case of unconstraint, Solver suggests the largest weight of 237.13% of J:HE@N(RI) with the highest return (2.69%). In case of constraint, in both 1st and 2nd half, Solver also picks the highest return stocks in large portions but is does not pick any stocks with negative weights for short sales due to the constraint that all the weights must be positive. The negative weights in case of unconstraint become zero in case of constraint. The largest positive weights in case on unconstraint remain the largest weights in case of constraint because those weights have minimal risks. This suggests that the largest weights chosen by Solver are consistent with the objective of maximizing portfolio returns and some stocks are weighted more heavily because they have higher returns among available stocks in the portfolio. However, Solver does not pick stocks by choosing from the highest return stock to the lower return stocks. For light weights, Solver tends to choose stocks with lower risks.
In case of unconstraint, portfolios are quite diversified and include all stocks to achieve the objectives. Solver tends to find the optimal solutions with a very large diversification to achieve the objective. Portfolios with minimal risks are more diversified than portfolios of maximal returns. In case of constraint, portfolios are also diversified but do not include all stocks. Portfolios with minimal risks are less diversified than portfolios of maximal returns.
Performance and portfolio strategy
Now we will discuss about the performance of 30-stock portfolio in the 2nd half. The feasible portfolios are portfolios of weights WMVP1U, WMVP1C, WOpt1U, WOpt1C and the perfect foresight portfolios are those of weights WMVP2U WMVP2C, WOpt2U and WOpt2C.
According to the calculation results, the feasible portfolios have much poorer performances than the perfect foresight portfolios. In general, the feasible portfolios have much lower returns but higher risks than the perfect foresight portfolios. For example, average return of feasible portfolios is -0.41% vs. 3.26%; average std. dev. of feasible portfolios is 11.01% vs. 5.45%; average sharpe ratio of feasible portfolios is 2.39% vs. 42.88%. The largest sharpe ratio of the feasible portfolio WMVP1C in the 2nd half is 11.53% which is smaller than all sharpe ratios of the foresight portfolios. This portfolio comes closest to the foresight portfolios because it has the highest sharpe ratio (or highest return) and the lowest risk among 4 feasible portfolios. In case of unconstraint, the best feasible portfolio is a feasible portfolio that comes very close to the WMVP2U foresight portfolio in terms of risk and return. However, for risk-averse investors, the best feasible portfolio can come near to WOpt2U portfolio because the return is highest among perfect foresight portfolios. In case of constraint, the best feasible portfolio is a feasible portfolio that comes very close to the WOpt2C perfect foresight portfolio.
Even though the data are from the last 10 years but we can see totally different effects of the 1st half data and the 2nd half data on the portfolios in the 2nd half. If we use the weights of optimal portfolios in the 1st half to evaluate the portfolio in the 2nd half, we do not get the same results. Moreover, the results obtained seem to be very far away from the results obtained by using the last 5 years data. This may be due to the fact that the 1st 5-year data, even if they are not so out-dated, do not reflect well the present market situation. When using such historical data we ignore recent changes in the market and therefore we might lose some opportunities. The performance of optimal portfolios in the part may be very far away from the perfect foresight portfolios. In fact, we can construct feasible portfolios by using past data but it is difficult to construct an optimal feasible portfolio where we can maximize returns and minimize risks. Even we can find such a portfolio, its performance is still far away from the perfect foresight portfolio
This suggests that we should not rely on diversification to match the performance of some market index to evaluate the performance of portfolios. We also should not assume that marketplace can reflect all available information in the market. Rather than relying on the simple diversification, we should take an active portfolio strategy, using available information and forecasting techniques to seek better performance and take advantages of the market such as finding mispriced securities.
Sally Jameson: Valuing Stock Options in a Compensation Package
Executive summary
Jameson needs to choose either stock option compensation package or cash compensation package if she joins Telstar. If she can sell her options during 5-year vesting period, the stock option package is worth more than the cash package. If she is not allowed to sell her option during 5-year vesting period, cash package is worth more than stock option package. In considering option liquidity, taxes and transaction costs, we conclude that cash package is worth more than stock option package and therefore, Jameson should choose cash package. If Jameson decided to choose stock option package, she should untie her wealth to the fortunes of Telstar by either entering a forward contract on stocks or using bull spread strategy to insure her long call position. In doing so, the value of her options will not totally depend on Telstar’ stock price. As a result, she can get some benefits even if her options turn to be worthless at expiration.
1. Options or cash compensation
a. Cash compensation:
If Jameson chose cash compensation package and if there is no tax, she will receive $5000 today. If she used this money to invest in 5-year T-bills, the future value of her compensation would be worth: $5000 x 1.0602 = $5301 in 5 years (5-year T-bills’ interest rate is 6.02% in the Exhibit 4).
b. Stock option compensation:
If Jameson chose stock options, she would hold European 3000 call options (early exercise is impossible) on stocks without dividends which give her the right to buy Telstar stocks at the strike price $35 per share in the 5th year from the date she joins Telstar. The option price is $2.65 (please refer to Appendix 01 for detailed option price calculation). Total value of 3000 call options that Jameson would receive is 3000 x $2.65 = $7943 (taxes and transaction costs are ignored), which is option premiums that Jameson can receive if she sells her 3000 granted options.
c. Cash or stock options?
If Jameson holds options until maturity:
- If Telstar’s stock price is below strike price ($35 per share), Jameson will not exercise her options and therefore will get nothing (she does not pay option premiums by cash).
- If Telstar’s stock price is above strike price, Jameson will exercise her options, sell shares and get profits = 3000 x (stock price – strike price).
- In order to have the same profit as that of cash compensation, the stock price must rise up to $5301/3000 + $35 = $36.767 per share.
- From the Exhibit 2, we see that Telstar’s stock price only rose to $35 per share in 1990 during the last 10 years. It means that the chance of the rise of stock price to above $35 par share is very rare. Therefore, if Jameson holds options until maturity, she will risk receiving nothing from the stock option compensation package.
If Jameson sells options after she joins Telstar:
- The profit from selling 3000 call options is $7943, assuming that there is no transaction costs, no taxes and it is easy to sell such options. As $7943 is greater than profit of cash compensation, we would say that stock option compensation is worth more than cash compensation.
d. Conclusion
If Jameson is free to sell her options at any time after she joins Telstar, and if there is no taxes and no transactions costs, stock options package is worth more than cash compensation.
2. Choosing the compensation package
It seems that option package is better than cash package. However, Jameson needs to consider other factors before choosing the best package.
- Options liquidity: Most companies granting stock options compensation packages do not allow their employees to sell options in the vesting period. There is no information in the case about the right to sell options. If Jameson is not allowed to sell her options at any time after she joins Telstar, she risks receiving nothing from option compensation package at the expiration time of options as discussed above. In other words, if she has to hold options until expiration, the value of her options would be easily zero at expiration.
- Early exercise: As options granted to Jameson are European calls, she can not exercise them before expiration. If she left Telstar before her 5th year with Telstar, she would get nothing. Her options will be, therefore, worthless to her.
- Taxes: If taxes are considered, Jameson will receive $5000 x (1-0.28) = $3600 today and $3600 + {$3600 x 6.02% x (1-0.28)} = $3769.04 in 5 years from cash package. In order to have the same profit as that of cash compensation, the stock price must rise above $3769.04/3000 + $35 = $36.256 per share. In such case, the value of her options must be at least ($36.256-$35) x 3000 = $3769.04. However, the chance of rise in stock price above $36.256 is even rare. As a result, taxes make the options be worthless easier. Besides, there is no advantage of tax treatment to her between cash package and option package as tax on Jameson’ salary would equal to tax on capital gains (28%).
- Conclusion: From the above analysis, we see that it is very easy that Jameson receives nothing if she chooses stock option package. Hence, she would better to choose cash compensation package. By doing so, she will have cash right after joining Telstar and will be free to leave the company if she finds a better opportunity.
3. Stock options compensation package from the view of granting companies
Employee stock options are the same as call options. Unlike call options, employee stock options are corporate securities issued by corporations. Corporations are the option writers and employees are option holders. Option holders pay strike prices to corporations when they exercise options. As a result, corporations will receive cash and issue new shares. At expiration, corporations will have more cash and more outstanding shares.
Granting stock options costs companies the value for which options are sold. In fact, companies do not pay for such value directly. Instead, this value will be deducted in employees’ cash compensation. In other words, employees pay for options value by receiving less cash compensation by an amount equivalent to options value. From the accounting view, this options value can be regarded as non-cash operating expenses to corporations.
Executive stock option plans create some incentives for their recipients:
- Tax reduction: as tax on individual income is higher than tax on capital income, stock options can help executives avoid tax payment on their high income and pay less tax on capital gains by converting part of their income to capital gains.
- Feeling of ownership: By granting stock options, the firm creates the feeling of ownership in the mind of its executives so they take actions in the interests of shareholders.
The purpose of creating incentive plans is to lure talented employees, keep excellent employees and motivate them to act consistently with the interests of shareholders with less cost to the firm. Stock option compensation plans have become popular nowadays because these incentive plans provide firms with several advantages:
- Minimize the firm’s compensation costs
- Conserve cash because the firm does not pay cash through option granting
- Avoid the limits on the tax deductibility of cash compensation
- Solve agency problems by aligning managers’ incentives with shareholders’ interests
While stock option packages bring granting firms with the above advantages, they are somehow worth for executives with high salaries but not worth for employees with low salaries. The biggest incentive of such compensation plans to receivers is to decrease tax payment on incomes. As discussed through the case of Jameson, it is very rare that employees can exercise options because the vesting period is long and options risk being worthless at expiration. It is, therefore, better that companies can create cash compensation programs that motivate employees and cost less.
4. Recommendations for Jameson
If Jameson accepts option package and works for Telstar, she should untie her wealth from the fortunes of Telstar by using bull spread strategy, which is to sell identical call options (option A) with higher strike price, for instance $40, to insure her long call position. Buy selling option A at $40 strike price, she can get option premiums. If Telstar’s stock price will not rise to $35, she will not exercise options granted by Telstar but can get option premiums to compensate her losses from not being able to exercise options. If stock price rises above $35, she will exercise options granted by Telstar and gain profits = stock price – $35. If stock price rises above $40, she will exercise options granted by Telstar and gain profits = stock price – $35 while delivering stocks to the holders of option A and get a loss = $40 – stock price. However, the overall profit when stock price is greater than $40 is positive. As a result, she can insure the benefits of her options regardless of increase or decrease in Telstar’s stock price.
The second way to untie her wealth to Telstar is to enter a forward contract in which she will pay a certain amount of money if stock price rises above $35 and receive a certain amount of money if stock price is below $35. If stock price is above $35, she has to give up a portion of the benefits from exercising options to pay the counterparty of the forward contract. If stock price will not rise above $35, she still gets money from the counterparty. By doing so, she can receive a certain amount of money regardless of increases or decreases in Telstar’s stock price.
| Appendix 01: Option price calculation | ||
| 1. Binomial Model | ||
| Assumptions: | ||
| 1. Single date: time 0 and time 1. | ||
| 2. Stock price can go up or down. | ||
| 3. Perfect market: there is no transaction costs, borrowing and lending at | ||
| interest rate, no taxes. | ||
| 4. Volatility on stock return is historical volatility that is assumed 30% based on Exhibit 3. | ||
| Calculation: | ||
| Current stock price (s) $ | 18,75 | |
| Divident yield (di) | 0 | |
| Volatility of stock return (sd) (historical volatility) | 0,3 | |
| Strike price (x) $ | 35 | |
| Time to expiration (t) years | 5 | |
| Risk-free rate (rf) % | 0,0602 | |
| Number of steps (n) | 1000 | |
| Price of European call option ($) | 2,92 | |
| Total value of 3000 options granted to Jameson | 8.760 | |
| VBA codes: | ||
| Function Euro_call(s, di, sd, x, t, rf, n) | ||
| 'calculate price of a Europeran call option by Binomial tree model' | ||
| Dim u As Double | ||
| Dim d As Double | ||
| Dim p As Double | ||
| Dim bicomp As Double | ||
| Dim sumbi As Double | ||
| Dim h As Double | ||
| Dim j As Integer | ||
| | ||
| 'calculate u,d,p' | ||
| h = t / n | ||
| u = Exp(sd * Sqr(h)) | ||
| d = Exp(-1 * sd * Sqr(h)) | ||
| p = (Exp((rf - di) * h) - d) / (u - d) | ||
| | ||
| 'calculate expected call payoff at time t' | ||
| For j = 1 To n | ||
| bicomp = Application.Combin(n, j) * (p ^ j) * ((1 - p) ^ (n - j)) * Application.Max(s * (u ^ j) * (d ^ (n - j)) - x, 0) | ||
| sumbi = sumbi + bicomp | ||
| | ||
| Next j | ||
| | ||
| 'calculate call price = PV of expected payoff' | ||
| | ||
| Euro_call = sumbi * Exp(-1 * rf * t) | ||
| | ||
| End Function | ||
| 2. Black-Scholes Model | ||
| Assumtions: | ||
| 1. Risk-free rate at 6.02% (Exhibit 4) is assumed to be known and constant in the next 5 years. | ||
| 2. There are no transactions costs and no taxes. | ||
| 3. It is possible to short-sell the options and and to borrow at the risk-free rate. | ||
| 4. Stock pays no dividend during the option life (5 years). | ||
| 5.Markets are efficients. | ||
| 6. Implied volatility is calculated by opserving market prices of the option. However, in this case | ||
| report, I assumed that implied volatility is equal to historical volatility at 30% and I ignored the | ||
| computation of implied volatility on stock return based on the information given in Exhibit 1. | ||
| This is because of the complexity of calculating and predicting implied volatility from information | ||
| given in the case. | ||
| Calculation: | ||
| Current stock price (s) $ | 18,75 | |
| Strike price (k) $ | 35 | |
| Volatility of stock return (v) (implied volatility) | 0,3 | |
| Risk-free rate (rf) % | 0,0602 | |
| Time to expiration (t) years | 5 | |
| Divident yield (d) | 0 | |
| Price of European call option ($) | 2,65 | |
| Total value of 3000 call options granted to Jameson, $ | 7.943 | |
| VBA codes: | ||
| Function Euro_callBS(s, k, v, r, t, d) | ||
| 'calculate price of a Europeran call option by Black-Scholes model' | ||
| Dim d_1 As Double | ||
| Dim d_2 As Double | ||
| Dim nd1 As Double | ||
| Dim nd2 As Double | ||
| | ||
| 'Calculate N(d1) and N(d2)' | ||
| d_1 = (Application.Ln(s / k) + (r - d + 0.5 * (v ^ 2) * t)) / (v * (t ^ 0.5)) | ||
| d_2 = d_1 - v * (t ^ 0.5) | ||
| nd1 = Application.NormSDist(d_1) | ||
| nd2 = Application.NormSDist(d_2) | ||
| | ||
| 'Calculate option price' | ||
| Euro_callBS = s * Exp(-d * t) * nd1 - k * Exp(-r * t) * nd2 | ||
| | ||
| End Function | ||
| 3. Option price | ||
| The option price by Binimial model is higher than the price obtained from Black-Scholes model. | ||
| Because it is very difficult to estimate accurately future implied volatility of returns on Telstar's | ||
| stocks in 5 years, the price by Black-Scholes model seems to be less reliable. | ||
| However, to be conservative, I chose the option price $2.65 by Black-Scholes model for the analysis | ||
| of the case. | ||
OPTION STRATEGIES AND CURRENCY FORWARDS
Question 01: Currency Forward
Where to lend and borrow?
Suppose we invest $1 in
Arbitrage
1. Borrow U.S dollars in the U.S, convert this amount to pounds and lend pounds in
2. Sell a forward contract in the amount of the proceeds of the investment amount in pounds back to US dollar.
Assume lending pounds at risk-free and interest paid one time at the end of the investment horizon. Below is an example of arbitrage:
Cash flow
Year 0 Year 1
$ £ $ £
1. Borrow dollars rus = 4% +1.6 -1.664
2. Convert to pound at $1.6/£ -1.6 +1
3. Invest in pound-denominated bonds -1 +1.07
at interest rate ruk = 7%
4. Sell a forward contract at £1.07 +1.6906 -1.07
value at today forward rate $1.58/£
Total 0 0 +0.0264 0
If we ignore the transaction cost, the arbitrage profit is $0.0264. The above transactions show that we can arbitrage with zero initial investment by borrowing US. dollars, converting into pounds and invest in pound-denominated bills. At the same time, we hedge against currency exchange rate risk by selling a forward contract. This arbitrage is call covered interest arbitrage.
Conclusion
If we want to invest dollars, there are 2 ways:
1. Buy dollar-dominated bonds in the
2. Exchange dollars into pounds, buy pound-denominated bonds and enter a currency forward contract to guarantee the exchange rate in which we will convert back pounds into dollars.
In general, the second way is preferable because we can gain arbitrage profits while hedging the position.
Question 02: Arbitrage Profit through Yen/U.S. dollar Currency Forwards
Yen/
From the perspective of a Japanese investor, the price of a 6-month Yen/U.S.$ currency forward contract is Fo,T = xo e(ry-rus).T (xo: exchange rate; ry : 6-month Japanese interest rate; rus : 6-month interest rate). In other words, Fo,T = 124.30 e(0.001-0.038)x0.5 = \122.0216.
Yen arbitrage profit
We ignore the transaction cost and assume lending at risk-free and continuous compounded interest during 3-month investment period.
Cash flow (million)
Month 0 Month 3
$ \ $ \
1. Borrow dollars rus =3.5% +1 -1.0088
2. Convert to Yen at \124.30/$ -1 +124.30
3. Invest in Yen-denominated bonds -124.30 +124.4555
at interest rate ry = 0.50%
4. Buy a forward contract at $1.0088 +1.0088 -124.3452
value at today forward rate \123.2605/$
Total 0 0 0 +0.1103
The Yen arbitrage profit is \0.1103 million.
Question 03: Long Strangle Strategy
· Donie should choose a long strangle strategy by buying out-of-the money calls and a puts with the same time to expiration to achieve the client’s objective. The reasons for choosing this strategy are:
- The premium of acquiring the position is minimum.
- The client expects an extremely high increase in volatility in the stock price of TRT Co. in either direction in response to the court’ decision.
· The long strangle strategy will provide the client with following benefits:
- Reward: Unlimited
- Profit: The potential maximum gain per share is unlimited when the substantial up and down movements of the stock are significant.
- Loss: The loss is limited to the cost of acquiring the position, which is the total premium paid for buying a call and a put option: $4 + $5 = $9.
- Breakeven stock prices: The breakeven happens when:
- The stock price (S) rises above the strike price of the call option ($60) by an amount equal to the cost of acquiring the position ($9). Or S> $69.
- The stock price (S) falls below the strike price of the put option ($55) by an amount equal to the premium paid to acquire the position ($9). Or S< $46.
Question 04: Transactions to obtain arbitrage profits without initial investment
Yen arbitrage profit with 0.0084 forward exchange rate
From the perspective of American investors. We ignore the transaction cost and assume lending at risk-free and continuous compounded interest during 1-year investment period.
Cash flow
Year 0 Year 1
$ \ $ \
1. Borrow dollars rus =5% +0.008 -0.0084
2. Convert to Yen at $0.008/\ -0.008 +1
3. Invest in Yen-denominated bonds -1 +1.0101
at interest rate ry = 1%
4. Sell a forward contract at $1.0101 +0.0085 -1.0101
value at today forward rate $0.0084/\
Total 0 0 +0.0001 0
The arbitrage profit is $0.0001 per Yen.
Yen arbitrage profit with 0.0083 forward exchange rate
Cash flow
Year 0 Year 1
$ \ $ \
1. Borrow dollars rus =5% +0.008 -0.0084
2. Convert to Yen at $0.008/\ -0.008 +1
3. Invest in Yen-denominated bonds -1 +1.0101
at interest rate ry = 1%
4. Sell a forward contract at $1.0101 +0.0084 -1.0101
value at today forward rate $0.0083/\
Total 0 0 0 0
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