A C T A U N I V E R S I T A T I S L O D Z I E N S I S FOLIA OECONOMICA 192, 2005
Iw o n a K o n a r z e w s k a *
SH O R T SALES AT W ARSAW STOCK EXCH ANG E PR E SEN T EXPERIENCE AND SO M E SIM U L A T IO N S
Abstract. The paper deals with present regulations and market conditions for short sales at Warsaw Stock Exchange. The history o f such transactions on the Polish market is very young - dates since January 1, 2000. The transactions are in use, till now, in a quite limited scale. We present theoretical considerations on estimating profit on short sales. Profit occurs as a result o f different attitude o f investors towards different financial investments decisions - time horizons, price expectations, utility functions etc. This form o f investment creates specific risk - the loss when the expectations do not come true. Possibility o f short sales transactions has also consequences for the optimal portfolio model - different portfolio composition as a result. Beside the characteristics o f present experience with short sales on the Polish market we present simulation results for portfolio investments allowing for short sales transactions. The results o f simulated investment strategy based on historical data have shown great instability o f estimates of profit for optimal portfolios with short sales allowed for the model with maximal slope (mean value over standard deviation o f the rates o f return) and possibility o f high losses. Moreover, we stress a great need for procedures helping in an optimal sample choice to estimate/forecast distribution parameters o f the rates o f return.
Keywords: short sales, portfolio investments. Keywords: JEL Classification: G i l .
1. INTRODUCTION
Let us intro d u ce a sim ple definition o f a sh o rt sale: a sh o rt sale is generally the sale o f a stock an investor does not ow n - it is borrow ed, sold and then b o u g h t after som e tim e to be retu rned to th e ow ner.
Investors w ho sell sh o rt believe the price o f the stock will fall. If the price decreases, they can buy the stock at the low er price an d m ak e a pro fit otherw ise they will m ake a loss. In the theory o f investm ents po rtfolio, allow ance fo r a sh o rt sale m eans th a t we do n o t lim it the solu tio n optim al
weights fo r portfo lio com ponents to non-negative values. T h e only constraint is th a t weights sum up to one. L intner (1965) introd uced the First “m ore realistic” 1 m odel o f sh o rt sales in p ortfolio theory - “ the sh o rt seller will receive interests at the riskless ra te r* on sales price placed in escrow, and he m ay o r m ay n o t also receive interest at th e sam e ra te on his cash rem ittan ce to the lender o f the stock. T o facilitate th e form al analysis, we assume th a t both interest com ponents are always received by the sh o rt seller, and th a t m arg in requirem ents are 100% ” (italics in original). L in tn er derives th e o p tim u m p o rtfo lio fo r th e in dividual in vesto r, assu m in g unlim ited borro w in g or lending a t the rate r*.
T h ere are various consequences o f sh o rt sales o n capital m ark e t. A m ong them we have to m ention its regulative influence o n prices causing increase o f supply on the m a rk e t and neutralizing speculative bubbles. It can be observed on the world m ark e t (cf. Staley 1997) a stro ng negative correlation betw een stock m ark e t price and the num ber o f open sh o rt positions. A t the sam e tim e it is said th a t high percentage o f sh o rt position s generally stim ulates the m a rk e t grow th - sh o rt sellers have to cover th eir positions which causes the price rise. G reat a m o u n t o f open sh o rt p o sition s can w ork as an in d icato r o f price overestim ation show ing th e existence o f divergence betw een price an d intrinsic value o f th e stock.
W e have to stress th a t sh o rt sales are connected w ith g reat risk and such decisions should be supp o rted by form er deep fu n d am en tal analysis o f th e firm and v aluation o f the stock. U sually in fo rm atio n a b o u t intention o f selling is secret - the consequence o f public d eclaratio n can be d ram atic and can even cause the bank rup tcy.
S h o rt sales tran sa ctio n s are often used as a p a rt o f m o re com plex investm ent strategies such as price arb itrag e strategy w ith futures contracts o n stock. T o decide ab o u t the strategy one should estim ate futu re value o f stock price and com pare it w ith present value o f fu tu re co ntract.
T h e aim o f this p ap e r is to show a brief history o f sh o rt sales in Poland and analyze the re tu rn on selected sh o rt sales tran sa ctio n s w hich happened du rin g the period 2.01.2003 - 31.03.2004.
2. SHORT SALES AT WARSAW STOCK EXCHANGE - MAIN REGULATIONS
O n D ecem ber 21 1999 - T h e C ouncil o f M inisters issued the regulations on d etailed principles, pro ced u res, term s an d c o n d itio n s o f b o rro w in g securities. A security w hich can be an object o f tra d e in sh o rt sales tran sa ctio n s should fulfill b o th the follow ing conditions:
• the m ean tu rn o v er calculated on the base o f last ten sessions is greater or equal to 1 m illion P L N ;
• ca p italizatio n n o t less th an 250 m illion PLN .
T h ere are tw o kinds o f agreem ents betw een p artic ip a n ts o f the trade: • the fram ew o rk borrow ing agreem ent - an agreem ent d eterm ining the procedure, term s and conditions o f m aking securities a subject o f borrow ing agreem ents, w here the borrow er is the b ro kerage house;
• the fram ew ork sh o rt sale agreem ent - an agreem ent d eterm in in g the p ro cedure, term s and conditions o f m aking securities a subject o f borrow ing agreem ents, w here the lender is the brokerage house.
T here are tw o kinds o f obligatory collaterals:
• collateral for the borrow ing - established by the b ro k erag e house as the borro w er, for the claim resulting from a borrow ing agreem ent concluded on the basis o f the fram ew ork borrow ing agreem ent;
• collateral for sh o rt sale - established by th e b o rro w er th a t sells borrow ed securities, for the claim resulting from a bo rro w in g agreem ent concluded on the basis o f the fram ew ork sh o rt sale agreem ent.
3. SHORT SALES TRANSACTIONS AT WARSAW STOCK EXCHANGE
We analyzed the d a ta available for short sales transactions, open positions in sh o rt sales th an k s to the N atio n al D eposit o f Securities web site fo r the period 2.01.2003-31.03.2004. In F igure 1 we present d a ta fo r six firm s present on sh o rt sales m ark e t in the analyzed period. W e can observe th a t investors were active during the period m ostly in selling sh o rt K G H M , Р Е К A O and P R O K O M shares. In the last 4 m o n th s o f the sam ple period we observed an intensification o f investors activity in selling sh o rt N E T IA shares. T ra n sactio n s on T P SA and PK N O R L E N shares were rare. In general, as it was announced by the N ational D eposit o f Securities, the value o f sh o rt sales tran sactio n s d u rin g 2003 was a little bit m o re th an 25 m illion PLN and the ra tio o f the sh o rt sale tran sa ctio n s value over to tal value o f tran sa ctio n s in shares was from 0.01% in A pril 2003 to 0.56% in July 2003. We noticed th a t alm ost after each session w ith a great num ber o f sh o rt sales tran sactio n s there was a significant rise in share prices possible to observe.
As it is generally difficult to analyze efficiency o f investm ents in sh ort sales, we have chosen several session days with large transactions in considered stocks. In o u r analysis we also to o k into account possible arb itrag e strategies w ith futures.
KGHM M 35000 г 30000 I 25000 ~ 20000 15000 I 10000 g 5000 0 TP SA PKN ORLEN PEKAO 30000 25000 20000 15000 10000 5000 0 03 .01.0 2 0 3.02 .14 0 3 .0 4 .0 1 03.05.20 03 .07.0 4 03 .08.2 0 03. 10. 06 0 3 .1 1 2 0 04. 01. 09 0 4 .0 2 2 4 35 30 25 S 20* 15
Fig. 1. Volume of short sales transactions and corresponding share prices - Warsaw Stock Exchange, 2.01.2003-31.03.2004
4. RISK AND PROFIT ON INVESTMENT STRATEGIES WITH SHORT SALES - SOM E EXAMPLES
We identified possible sources o f profit on investm ent strategies including sh o rt sales transactions:
positive em pirical verification o f an expected fall o f share price a t the d ate o f closing the position;
• possibility o f a m ore effective portfolio construction taking into account interdependencies am ong rates o f retu rn on securities;
R isk on capital m ark e t can be defined as a p ro b ab ility th a t the return on investm ent will be below the level the investor does n o t wish the returns to fall. R oy safety first criterion is to m inim ize such p ro bability. W hat sources o f risk can be identified when an investor uses s h o rt selling strategy? We will distinguish som e o f them :
• expectations o f falling price were n o t sufficiently su p p o rted by the fun d am en tal analysis o f the firm;
• m islead in g in a c c u ra te forecasts o f price fall (n o t a d e q u a te price forecasting m odel, choice o f statistical sam ple and dynam ic changes o f statistical characteristics, unpredictable events, etc.);
• bad choice o f m om ents for sh o rt selling and closing positions; • a call for stocks before the d ate in the borrow ing agreem ent. N ow let us analyze som e historical cases.
4.1. Selling short P R O K O M stocks
Since 24.06.2003, as we can see in F igure 2, we observed a fast increase in the n u m b er o f open positions in sh o rt sales from 2700 shares to 17 000 on 1.08.2003. O n 19.09.2003 15 100 positions were closed. W as there a high expectation o f price fall?
Fig. 2. Number of open positions in short sales of PROKOM shares during 2.01.2003-31.03.2004
M ea n sh o rt selling price in the period 24.06 - 1.08.2003 (29 sessions) calculated as the w eighted average was 146.24 P L N . T o ta l n u m b e r o f shares sold sh o rt d u rin g th a t period was 19 570. T o ta l incom e from sh o rt selling o f 15 100 (this is the n um ber o f positions closed on 19.09.2003) shares was equal to 2 208 168.60 P L N . T he share price on the closing d ate was 174.50 P L N which m eans th a t the to tal cost o f closing sh o rt po sitio ns was
2 634 950 P L N . In consequence we have observed a to tal loss from sh ort selling equal to 426 781.40 P L N , th a t is about 28.26 PLN per share. C hoosing for instance 1.10.2003 as a closing position d ate would bring a loss ab o u t 17.26 PLN per share. W e did n o t analyze tran sactio n costs - the loss was even higher. 195 185 175 165 155 145 135 125 / л 1V# V\ _ \ / • V y t * __ - - - . FPKMU3 * X % 'o. *
4
4
4
* * * \ ^ ^ \
% % %
Fig. 3. Stock prices and prices of futures FPKMU3 o f PROKOM during 24.06.20U3 19.09.2003 (exercise date: 19.09.2003)
Fig. 4. Volume o f futures FPKMU3 during 3.06.2003-19.09.2003 (exercise date: 19.09.2003)
W e p resent in F igure 3 stock prices an d priccs o f fu tures co ntracts F P K M U 3 (with exercise date 19.09.2003) - the only contracts traded between 24.06 - 1.08.2003 on P R O K O M shares. F ig ure 4 illustrates volum e of co n tra cts possessed by investors d u rin g he period w hen co n tra cts were on the m arket, 3.06. - 19.09.2003. T he date 1.08.2003 corresponds to the m aximal n um b er o f possessed co n tracts - 23 300. O n the exercise d ate 19.09.2003 the n u m b er o f co n tracts was 16 100. It m eans th a t 15 100 fu tu res co ntracts could have been p arts o f arb itrag e strategies w ith sh o rt sales. A nalyzing a re tu rn o n possible arb itra g e strategy including futures we have found th a t
m ean value o f considered futures co n tra cts was 138.27 P L N . M ultiplying the m ean price o f co n tra ct by 15 100 gives to tal co st o f 2 087 803.26 PLN . C o m p arin g th e cost with total incom e from sh o rt sales results in 120 365.34 PLN o f pro fit, alm ost 8 PLN per sh are2.
A n obvious conclusion follows: on the rising stock m a rk e t we can m ak e profits by em ploying arb itrag e strategy com bining sh o rt sales w ith futures contracts.
4.2. Selling S hort T P SA Stocks
200 th o u san d s o f stocks were sold sh o rt o n 21.08.2003. T h e m ark et stock price was 15.75 P L N . Positions were closed on 1.09.2003; the stock price was 16.75 P L N . A nalyzing a simple strategy o f sh o rt sale we should conclude th a t a loss o f 200 000 P L N was observed. L ater o n 20.09.2003 the stock price fell to the level 13.75 P L N . L o o k in g a t prices o f futures c o n tra cts traded in A ugust we found F T P S U 3 w ith exercise d a te 19.09.2003 and F T P S Z 3 with exercise d ate 19.12.2003 with m ean price a b o u t 15.39 P L N . A nalyzing p ro fit on possible arb itrag e strategy with fu tures, assum ing th a t investors had to sell possessed futures co n tra cts earlier th a n on the exercise d a te - it was observed th a t 225 000 futures F T P S U 3 co ntracts were sold on 29.08.2003 at the closing price 16.75 P L N . We conclude th at investors earned profits, which can be calculated (om itting tim e value) as follows:
total income on short sales (200 000-15.75 PLN) 3 150 000 PLN -cost of futures contracts (200 000 -15.39 PLN) 3 078 000 PLN + income from selling futures contracts (200 000 ■ 16.75 PLN) 3 350 000 PLN -cost of buying stocks on the market (200 000 • 16.75 PLN) 3 350 000 PLN
profit = 72 000 PLN.
C oncluding, it was a n o th e r exam ple o f p ro fitab le investm ent strategy.
5. PORTFOLIO INVESTMENTS WITH AND WITHOUT SHORT SALES ALLOWED AT THE WSE
Let us in tro d u ce the follow ing n o tatio n s used in fo rm u latin g optim al p o rtfo lio m odels:
• x = [x t , x 2, ..., x j - a vector o f fraction s o f the p ortfo lio funds invested in n assets;
2 We did not take into account the value of time in our calculations - the profit is a little bit lower.
• R p = Yj x f t i ~ a po rtfolio rate o f retu rn , R t - rates o f retu rn on 1 = 1
individual assets;
• X - a covariance m a trix o f n rates o f return; • <Tp = xTL x - a portfolio variance.
W e em ployed tw o kinds o f optim al p ortfolio m odels: m inim um portfolio variance m odel and m odel w ith m axim al slope - w here slope was defined as a ra tio o f p o rtfo lio rate o f retu rn and p ortfolio stan d ard d eviation. The only co n stra in t was sum o f fractions equal to one and for m odels w ithout sh o rt sales we required nonnegativity o f fractions. T h e m odels are presented in T ab le 1.
Table 1. Optimal portfolio models
Specification Short sales not allowed Short sales allowed
Min variance models min a 1 min a*
ST ST
E * i = 1 £ * , = 1
x, > 0 i = l , 2, ..., n
Max slope models Rr R,
max — max a r S T ST E*. = 1 U —1 i - 1 x, > 0 i = l, 2, ..., n
T h e aim o f the historical sim ulation experim ent was to check the dynam ic behavior o f optim al solutions o f the m odels. W e based sim ulations on em pirical d a ta o f stock prices for 19 firm s included in W 1G20 index. We distinguished 8 sam ple periods:
• Ja n u a ry -J u ly 2003; • M a y -N o v e m b e r 2003; • F e b ru a ry -A u g u s t 2003; • Ju n i-D e cem b er 2003; • M a rch -S ep tem b er 2003; • Ju ly -Ja n u a ry 2004;
• A p ril-O c to b e r 2003; • A ugust 2003, F eb ru a ry 2004. F igure 5 presents optim al portfolio frontiers for m odels with and w ithout s h o rt sales as well as stocks o f individual firm s which were tak en into a c co u n t using d a ta for the last sam ple period. It illustrates th a t solutions for m odels allowing for short sales dom inate the solutions fo r m odels without sh o rt sales. T h e result is very prom ising for sh o rt sales ap p lication s in capital investm ents.
F ig ures 6 an d 7 p resent dynam ic solutions fo r m odels w ith and w ithout s h o rt sales for m inim um variance and m axim al slope respectively.
m ea n ra te of re tu rn
Fig. 5. Optimal portfolio frontiers for models with and without short sales (August 2003-February 2004)
distance: short -
no short standard deviation ■ n o s h o r t - s h o r t
E 0.8% f 0.7% 'S 0.6% o> я 0.5% n 0.4%0.4% Q) 0.2% 4— 0.5% 1.0% 1.5% 2.0% 2.5% 3.0% Standard deviation n o s h o r t - ® - s h o r t
Fig. 7. Optimal portfolios for maximum slope models for 8 sample periods
Som e conclusions draw n for optim al solutions o f m inim um variance m odels are as follows:
• b o th kinds o f m odels - with and w ithout sh o rt sales - have shown th a t results are very sensitive to the choice o f the sam ple period;
• we have observed increasing tendency o f p o rtfo lio risk estim ates; • faster increase o f risk estim ates characterizes p o rtfo lio s w ith ou t short sales;
• m inim um variance portfolios with sh o rt sales alw ays presented lower stan d ard deviations and a t the sam e tim e lower m ean retu rn in com parison with m odels w ithout sh o rt sales.
A nalyzing dynam ics o f optim al solutions for m axim al slope m odels we conclude:
• results o f optim izatio n m uch differ fo r m odels w ith and w ithout sh o rt sales;
• characteristics o f portfolios with sh o rt sales occurred m o re sensitive to the sam ple choice;
• po rtfo lio s w ith s h o rt sales have show n a tendency o f rising retu rn w ith corresp o n d in g higher risk;
• portfolios w ithout short sales were also sensitive to the sam ple choice b u t presented a tendency to dim inish re tu rn with co rresp o n d in g grow ing risk in time;
• the distance between optim al portfolios with and w ith ou t sh o rt sales is grow ing.
We condu cted also a sim ulation o f profits on p o rtfo lio investm ents. T he steps o f the calculation procedure were the following:
• calculate estim ates o f stan d ard deviations an d covariances am ong securities;
• calculate optim al p ro p o rtio n s o f investm ents on individual securities; • sim ulate “ o p tim a l” investm ent on the first session o f the m o n th follow ing the sam ple period and closing the positio n on the first session next m o n th .
T h e experim ent revealed the weakness o f such naive strategy - it is very risky. F o r m inim um variance m odels m ore losses were observed for “ optim al” portfolios w ith o u t s h o rt sales. F o r m axim um slope m odels estim ates o f profit w ere very unstable especially for “ o p tim a l” p ortfo lio s with short sales. T h e results arc presented in F igures 8 and 9.
□ n o s h o r t ■ s h o r t
6. FINAL REMARKS
It was difficult to notice positive return s on sh o rt selling individual securities at W SE d u rin g the analyzed period Ja n u a ry 2003 - M arch 2004. N evertheless, we have show n the efficiency o f som e arb itra g e strategies with futures co n tra cts which gave high profits to investors. T h e m ark e t was rising in general in the analyzed period - on the rising m a rk e t com bining s h o rt sales with futures con tracts can m ak e profits. T ra n sactio n s on sho rt selling are still rare - average num b er o f securities with open sh o rt position was 8, while m ore th an 30 were allowed for sh o rt selling. In o u r analysis we did n o t include collaterals and com m issions paid and value o f tim e w hich is needed in m ore precise calculations o f p rofits o n investm ent strategies. We should stress the need for procedures helping in optim al sam ple choice to estim ate/forecast return s, deviations, covarian ce stru ctu re am o n g securities.
REFERENCES
Lintner, J. (1965), “The Valuation of Risk Assets and the Selection o f Risky Investments in Stock Portfolios and Capital Budgets”, Review o f Economics and Statistics, February, 13-37.
Markowitz, H. M. (1987), Mean-Variance Analysis in Portfolio Choice and Capital Markets, Oxford: Basil Blackwell.
Staley, K. F. (1997), The A rt o f Short Selling, New York: Wiley, translated into Polish:
Krótka sprzedaż. Jak czerpać zyski z niepowodzeń spółek, tłum. J. Juruś, Kraków: Oficyna
Ekonomiczna, Dom Wydawniczy ABC, 2001.
Iwona K o n a rzew sk a
KRÓTKA SPRZEDAŻ NA GPW W WARSZAWIE: DOTYCHCZASOWE DOŚWIADCZENIA, KILKA SYMULACJI
(Streszczenie)
W artykule omawiamy dotychczasowe uregulowania i warunki funkcjonowania krótkiej sprzedaży na GPW w Warszawie. Historia takich transakcji na rynku polskim jest krótka, datuje się od 1.01.2000 r. i stosowane są one, na razie, w dość ograniczonym zakresie. Przedstawimy teoretyczne rozważania na temat szacowania zysków ze stosowania krótkiej sprzedaży. Zyski pojawiają się tu w wyniku różnego podejścia inwestorów do inwestycji w papiery wartościowe - różne horyzonty inwestowania, inne oczekiwania odnośnie do kształtowania się kursów. Z tą formą inwestowania wiąże się także specyficzne ryzyko - strata w przypadku gdy oczekiwania się nie spełnią. Możliwość krótkiej sprzedaży papierów wartościowych ma swoje konsekwencje dla modelu optymalnego portfela inwestycji finansowych - prowadzi do
wyboru innego składu portfela. Analizujemy również portfele konstruowane z wykorzystaniem kontraktów futures. Obok charakterystyki dotychczasowych doświadczeń z tą formą inwestowania na rynku polskim przedstawiono wyniki symulacji zysków z inwestycji portfelowych z uwzględ nieniem krótkiej sprzedaży. Pokazały one dużą niestabilność ocen zysków z optymalnych portfeli inwestycyjnych z wykorzystaniem krótkiej sprzedaży i możliwość występowania dużych strat. Podkreślamy ogromne znaczenie algorytmów optymalnego doboru próby dla estymacji i pro gnozowania parametrów rozkładu stóp zwrotu.
