國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
28
33 8021 Topoint* 27 Long 25.8 6.500888889 167.7229
34 8201 BESTA* 11.9 Long 10.9 1.037310924 11.30669
652.0504
Trading Strategy II
To avoid selection bias, we singled out the stock whose V(Mc) to share price ratio lies between one and three. This is because there is little chance a stock price will rise or drop 300 percentages in only two weeks. The second reason is because the higher V(Mc) to share price ratio indicates the higher shareholder value. On the other hand, it may expose that the firm is in the inappropriate liquidation management condition.
For trading strategy II, we do not leverage by establishing both long and short position simultaneously since short positions are generally initiated by more adventurous and advanced investors. Trading strategy II is a relatively passive investment strategy suitable for conservative investors. It doesn’t need to create a large portfolio nor obey margin requirement. Instead, the only thing the investors have to do is to select the stocks which fall within the interval. Here, we simply long the stock whose V(Mc) to share price ratio falls between one and three. After selecting the stocks, we buy ten lots of stocks for each on 2015/05/14. Table VII summaries the data collected for the trading.
‧
Table VIII：the analysis of the trading strategy II (case A)
# stock holding returns for the period. Table VIII shows the results of our transaction. We use simple return17 to calculate the return on the investment. As we can see at Table VIII, only three out of ten stocks decreased in value, which are Chroma, Aurotek, and BESTA. Overall, trading strategy II has a gross profit of NT$80,700 and the rate of return is nearly 10 percent. Individually, stock 3450 yields the biggest payoffs, rising 34 percent to NT$186.5 while BESTA drop 8.4 percent to NT$10.9. Using weighted average formula, we find out that, among all the stocks ELASER performed the best, accounting for 5.5 percent of the total return. VOLTRONIC ranked the second-best performing stock with 10 percent rising in stock price and 2.2 percent increase for the total return.
17 simple return(ROI)=net proceeds/total cost=(Earnings-initial investment)/ initial investment
‧
Table IX：the transaction and the results of trading strategy II of case A
# stock
symbol
Company
value of position
on 2015/05/14 Shares value of position
on 2015/5/29 ROI
Shareholder value is also computed by Mc, but it contains liquation value.
We make an alteration on the model, assuming there exists a liquation value, that is when M = 0, the firm is in financial distress. If the firm is liquidated at the time when M = 0, it will have salvage value LT. Hence the shareholder value function Vt is equal to the expected present value of total discounted dividends up to the bankruptcy date T plus the liquation value. Thus we rewrite (10):
Vt ≡ f(Mt) ≡ E [∫ e−r(s−t)θ(Ms)ds|Mt
T
t
] + e−r(T−t)LT (30)
where r denote the appropriate discount rate and T as the time when M = 0. Other notations for the variables are the same as the ones mentioned in section 3. We reset (11):
‧
Following the previous proving process, equation (10) will become
constant ≡ E [∫ e−rsθ(Ms)ds + e−rtVt
Since e−rtLT is a constant, we differentiate the equation (31) with respect to t will get the same result as that equality holds in (11). We later follow the derivation process of the formulas demonstrated in Section 3, the equation (19) satisfies two boundary conditions:
1. When cash reserves falls to zero, the firm is on the verge of bankruptcy and it don’t have extra money to finance its business. Although the firm can survive via negotiating a line of credit18 with the bank, it is still on the line. The value the firm left when the cash reserves falls to zero is its liquidation value. L0 is the liquidation value at time t.
V(0) = ω1+ ω2 = L0 (33)
2. When M reaches the target threshold M∗ , the firm will start to distribute all the excess money and thus the marginal value of cash is 1.
18 An arrangement between financial institution and a customer that establishes a maximum loan balance that the bank will permit the borrower to maintain.
‧
Using the results of (35) and (36), we obtain the shareholder value as
V(M) =e βM− e αM− L0αe αM∗e βM+ L0βe βM∗e αM
βe βM∗− αe αM∗ (37)
Using accounts on the balance sheet, we define the liquation value as:
liquation value19
= short − term investment + accounts receivables
+ other receivables + prepaid expense + other current assets + other assets + inventory ∗ 0.8 + long − term investment ∗ 0.7
19 Asset liquidity is the degree to which assets can be sold. The easier the assets can be turned into cash, the more liquid the assets are. Therefore, we multiply each asset by one or a constant below one to represent the ease of liquidity. For example, fixed assets like plants and equipment are less liquid, so the weight assigned to the asset price is less as well.
20 All debts=current liabilities + long-term liabilities + other liabilities
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
33
M0 and zero, indicating that the firm experience financial distress. The marginal value of cash for shareholder in this regime is especially high.
Figure II：the shareholder value function (with liquidation value)
For simplicity, we assume V(ML) per share is equal to V(ML) divided by numbers of shares outstanding. Table VIIII summarizes the comparison of the estimates to actual share price on 2015/05/14. Compare the same company profile listed on Table IV and Table VIIII, we may find out that adding liquidation value mostly increase the shareholder value. For example, Everspring’s V(ML) per share is three times larger than its V(Mc) per share, while the ratios of V(ML) per share to V(Mc) per share of other companies are close to one.
Shareholder value
M
(cash reserves) M0
‧
Table X：the comparison of V(ML) per share and share price on 2015/05/14
# stock symbol Company V(ML) per share Share price on 2015/05/14
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
35
Trading Strategy I
Following the same instruction and assumption in case A, we first compare the differences between the V(ML) per share and the share price on 2015/5/14, and then construct an arbitrage-based trading strategy designed to exploit small differences.
We long if the V(ML) per share is higher than the share price, while short equities that the V(ML) per share is lower than the share price. The numbers of shares we buy were determined by the V(ML) per share divide by the share price on 2015/05/14. The analysis is shown at Table V. It shows that we have long position in 30 companies, and the estimated total long position cost NT$ 5,556.92, which is greater than the amount of money spent in case A.
The determination of the number of short sale shares is also same as case A. Table X summarizes the results of the transaction we made on 2015/5/14 based on the V(ML) model. Judging by Table X, we hold short position in stock 2390, 2497, and 3018. From Table X, it is particularly noteworthy that V(ML) per share of PCM is negative, which suggests it may go bankrupt based on our model and cannot be traded in open market, we therefore do not hold or borrow any of its stocks. The star symbol appeared at Table XI denotes the stock which is losing value during the holding period.
‧
Table XI：the analysis of the trading strategy I (case B)
# stock symbol Company V(ML) Share 7 2390 Everspring 6.2378 27.6 Short 0.226007246 3177.463772
8 2404 UIS 175.8707 35.1 Long 5.010561254 -175.8707 17 2495 Infortrend 111.4988 16.75 Long 6.656644776 -111.4988 18 2497 E-LEAD 52.1568 67.7 Short 0.770410635 932.1390499
‧ 國
立 政 治 大 學
‧
N a tio na
l C h engchi U ni ve rs it y
37
33 8021 Topoint 175.5492 27 Long 6.501822222 -175.5492 34 8201 BESTA 20.2497 11.9 Long 1.701655462 -20.2497
Table XI record the amount of money we earn or spend on every trading occurred on 2015/5/29. On the date, we sell the identical number of shares to neutralize the long position while purchasing back the stocks to offset the short position. By doing so, we incur capital gains of NT$788.2747. Observing the trading record from both case A and B, it’s easy to find out their portfolio are extremely similar. The major difference is that case B has relatively more long position besides stock 2404. However, case B does not own a short position in stock 3043. The differences of their profits attribute to stock 2390, 2497, 3018, and 3043. For risk assessment, we don’t hedge in both cases, implying that we may suffer losses once the stock price of our long position goes down or the stock price of our short position soars. Since the size of short position in case B is bigger, which suggests case B is more risky21. In short, case A and B prove the shareholder value is one of the reliable methods on identifying a firm’s true value.
21 Logically, there is no upper bound of capital losses in a short position because there is no maximum restriction on a stock’s price.
‧
Table XII：the results of the trading strategy I (case B)
# stock
22 Same as before, the star symbol denotes the stock which is losing value during the holding period.
‧
real stock market condition in Taiwan, the trading volume for each stock is ten lots.Table XII summaries the information of trading strategy II. Compared to case A, case B portfolio includes 9 different stocks instead of 10. Moreover, by selecting stocks from the criteria we use in both cases, we get similar result patterns－that is, to invest in stocks 2360, 2482, 3030, 3450, 3665, 6215,6409, and 8201. Namely, the difference of their performance only depends on the stock 2312, 2461, 2474.
Table XIII：the analysis of trading strategy II (case B)
# stock
‧
Table XIII shows the results of our transaction, including the analysis of the return on investment. The transaction of case B has an approximately gross profit of NT$92,300 and its return on investment is about 8 percent. The top three percentage gainers among these nine stocks are ELASER, BHI, and TRI, which rose 34 percent to NT$186.5, 10 percent to NT$146.5, 9.6 percent to NT$67.6, respectively. As for the stock performance in the investment, ELASER, VOLTRONIC, and BHI are the top three, accounting for 4 percent, 1.6 percent, 1.1 percent each. The fact that case B has lower return on investment yet generates more profits than case A is due to the initial investment.
Table XIV：the transaction and the results of trading strategy II (case B)
# stock
symbol
Company