Relative valuations in options

Recently, while updating my CV, I was forced to ponder what I have done during my stint at BACS. One thing that came across my mind is charlatanesque relative valuations of options. Universally options are priced using the closed form Black Scholes model. Some of the relative valuation techniques are as follows:
Skew vs. Implied Volatility: Normally, a strong relationship is seen between implied volatility and volatility skew (especially skew based on sigma). Hence a scatter plot of current skews and IVOLs of indices / single names will reveal indices / singles that are way off from the relationship and risk reversal trades can be put work on the outliers
Skew vs. Open Interest (OI): While skew is the premium paid by an investor / trader for his negative sentiment, the OI Put Call Ratio (OI PCR) measures the negative sentiment from open interest perspective; a parallel can be drawn between premium and price, and similarly between OI and volume. We know that in any asset market if increase in the price of the asset is not accompanied by rise in volume then the price increase won’t sustain for long. In similar vein if rise in skew is not accompanied by rise in OI PCR then the skew can be expected to drop. Hence whenever there is a divergence between skew and OI PCR then a trade (short / long strangle) can be put to work. For instance termstructures of skews and OI PCR can be plotted and if for certain maturity the skew is relatively higher than OI PCR then straddle / strangle of that maturity can be sold
Sectoral Volatility Premium (SVP): It is nothing but the spread between implied volatility of a sector index and that of the broader market index, for instance the implied volatility spread of XLV (pharmaceutical ETF) and SPY (S&P 500 ETF). This SVP can be used trade sectoral volatility across regions. For instance the US and Europe markets are almost similar and after looking at the historical relationship between pharmaceutical SVPs of US and EU a volatility spread can traded if any divergence exists. Similar spread trades are also possible between related industries like Semi-conductor vs. InfoTech, Oil refiners vs. Oil rig companies and so on. By trading SVP, the broader market risk and company specific risks are hedged off. SVP can also be used to trade sector rotation

Above techniques are within the ambit of the volatility market; following techniques are relative valuations across markets.

Earnings Yield Premium vs. Implied Volatility: This technique compares values between volatility and equity markets. The expected return / risk premium for an equity is calculated using CAPM though this model is useless for an index. Hence for sake of simplicity in the case of single names and for lack of any model for index the inverse of PE ratio would be used as expected yield of the equity/index. The implied volatility measures the risk of the asset and hence to make an apple to apple comparison the earnings yield is adjusted for the government bond yield to get the risk premium which is another measure of risk of the asset. Since implied volatility and earnings yield premium both measure riskiness of the equity / index and it is seen that strong relationship exists between these two. Hence EYP and IVOL can be used for relative valuation between equity and volatility market
Credit Default Spread vs. IVOL: This is based on the idea propounded by Merton which gained wide popularity especially during the subprime crisis. During the crisis option traders who found options trading at extreme quotes preferred CDS to hedge their portfolios. While the relationship between EYP and IVOL is straight forward as the underlying asset is equity (though tenures differ), the same can’t be said about CDS vs. IVOL. In this case Miller & Modigliani have certain say. Though strong relationship is seen between IVOL and CDS for low rated companies, especially junk rated companies, the relationship is weak for strong companies (highly rated companies). So balance sheet plays an important role in the relationship, weak balance sheet strengthens the relationship between CDS and IVOl, and vice versa. Another factor that weakens the relationship between CDS and IVOL is again the tenure.

A critique of Credit Suisse Fear Barometer (CSFB) index (uptd)

Credit Suisse recently launched a fear index, Credit Suisse Fear Barometer (CSFB Index) which the firm expects to replace the most prominent ‘fear’ index, VIX. The idea behind the CSFB Index is to quantify fear by putting a zero premium collar on the underlying asset. This combination trade consists of selling a call option of strike 10% above the spot by receiving Rs. X as premium and buying a put of strike Y% lower than the spot by paying a premium of Rs. X, thereby the initial net outlay is zero. The owner of the combo trade is ready to sacrifice gain exceeding 10% in return cuts the loss to the maximum of Y%. The CSFB Index is nothing but this ‘Y’. The report’s contention is that more the Y% lesser is the protection one is getting hence this is an indicator of fear. Following are counter points that argue against the claim that CSFB Index is better than VIX.

• For the above italicized assumption the counter could be that when Y% > 10% the trader won’t put in a collar trade unless he is bullish since he would be betting 10% upside against Y% downside. We see that the CSFB index peaked before the crisis as the traders were over confident or irrationally exuberant. Hence prima facie the index is not reflective of fear among investors
  
  

• The price of an option is a function of five factors as per Black Scholes and measuring fear just by price is flawed. The interest rate, an often ignored factor, justifiably over short period can’t be ignored when developing an index as the prices are impacted by the prevailing interest rate regime. When interest rate rises and other factors maintain status quo put price declines while call rises. We know that Call = S * N(d1) – PV (Strike) * N(d2) and Put = PV(Strike) * N(-d2) – S * N(-d1) and as interest rate rises PV(Strike) declines hence price of put decreases and that of call increases. And hence for the collar trade the trader might have to go deep Out of The Money (OTM) which increases Y% which in turn leads to rise in the index. We see that though the index is choppy both the index and 3 month government yield trend together. The argument is that though interest rate is comparatively minor factor during high interest rate regime it certainly matters in pricing options
  

Since the index lacks fundamental backing it pales as a measure of fear against VIX. On the contrary the index can be used assess the level of irrational exuberance among investors.

VIX – VXO Spread: Risk appetite & diversification (uptd)

Today’s chart looks at SPX Index since January 1995 overlaid with spread between VIX and VXO. VXO is implied volatility index for S&P 100 index and VIX is for S&P 500; S&P 100 is index of 100 companies and S&P 500 is of 500. Hence VIX will trade at lower levels than VXO as the former has higher degree of diversification than the latter. And investors’ preference for diversification depends on investors’ risk appetite - during episodes of high risk averseness investors prefer diversification hence prefer S&P 500 over S&P 100 there by the spread narrows and we see that during the bout of high risk averseness the spread plunges into negative zone. When risk appetite increases the spread increases and trade above zero as seen during 2005-07. Over the last five trading sessions VIX exceeded VXO which shows that risk appetite of the investors are on rise which is good for the market. Another take from the chart is that despite current crisis being termed as one of the worst recessions since the Depression the retracement of risk aversion has been narrower compared to the ‘V’ of Tech bubble crisis.

Gold, a bubble?

Yesterday, gold closed at USD 1145, the historical high, and the metal over last 12 months has generated a return of more than 50%, outperforming the broader equity market by more than 18%. The following charts look at relationship between gold price and an index that is proxy for gold price, and also evolutions of these two.

Gold is an asset which is primarily used as a hedge against inflation and also as a hedge against crisis i.e. investors seek gold when the risk averseness increases. On the other hand gold is an anathema during strong growth period. Hence price of gold theoretically should be proportional to risk averseness and inflation, and inversely related to growth. Based on this premise an index as proxy for gold price was devised as follows,
Gold Proxy Ratio Index = (1 + rp) * (1+ Πe) / (1 + ge)
where,

rp - risk premium (difference between SPX’s earning yield and 5 year US Treasury yield)

Πe - expected inflation (breakeven from 5 year Treasury Inflation Protected Securities, TIPS)

ge - expected growth (yield of 5 year TIPS)

The scatter plot shows that since August the relationship has deviated from the normal course in favour of gold price hinting that the recent run up seen in gold might be a bubble in formative stage. The line chart too shows a considerable divergence between gold price and the proxy.

Thenkulam Index

From technical perspective market is said to be strong if demand for stocks rises despite increase in stock price and volume declines as the price slides. The following chart shows the relationship between stock price and volume traded in a strong market

In a weak market the relationship gets reversed, volume increases as price declines and vice versa. The following chart shows relationship between price and volume traded in a weak market


Based on these premises a new technical analysis too is developed to gauge the strength of the market which is ratio of % change in price and % change in volume. In strong market the ratio will be positive and negative otherwise

Fine tuning the tool further the Thenkalam Index looks at relative strength temporally; the derivation is as follows
· X = 1 if the ratio is positive (i.e. the market is strong) and 0 if the ratio is negative
· Thenkalam Index = 20 day MA of X – 40 day MA of X

If the index indicates that the market is stronger when the index rises above zero and weaker when the index is below zero (refer to the chart given above)

The following chart shows the difference between 5 day moving average and 10 day moving average. We can see that the market broadly rallies after a spike in the index

Crude's supposedly demand curves

Despite the significance the chart is flawed since demand curve factors price and quantity, and not time.
I am trying to integrate time into demand and supply curve which will most probably result in cyclical pattern from a '8' shaped loop. The second chart is just part of this step

U to W by Keynes

Keynes & shapes of recession

Just few months ago the world was swamped with images of the Great Depression. Thanks to media, each and every one who had access to 24X7 TV networks knew what a recession (if not depression) as financial analyst / economist took extra effort to showcase there awareness on the Great Depression and recession. The resurgent market and reviving economy has taken everyone by surprise and it seems that Keynes has rescued the global economy once again from depression; 70s saw ‘W’ shaped recovery which possibly could have been another painful ‘U’ shaped recession. The chart shows US's Federal deficit overlaid with shaded areas for NBER's recession. It seems that Keynes apart from changing 'U' to 'W' (shape of recovery) has also lowered the frequency of recessions.