The Application of Gold Price , Interest Rates and Inflation Expectations in Capital Markets

The aim of this research is to determine a forecasting model of the price of gold in relation to the rate of interest from 1971–2013 that would benefit wealth managers in their forward interpretation of capital market expectations. It is not a model for market makers, since the price-setting dominance of banks in the physical as well as derivative markets presents a problem for any economic agent participating in these markets. Nonetheless, the ability to understand the variability of gold, interest rates and prices would clearly enhance financial planning and investor performance. This research models a full population of the price of gold with the rate of interest, in order to assess what impact a change in the interest rate would have on a change in the gold price (and vice versa). In developing a model price of gold that is strongly correlated with the actual price, the outcome of the research expects to show that not only is the interest rate and the gold price manipulated in relation to each other, but would also affirm the Gibson’s Paradox, that real gold is inversely related with the real interest rate, so that real prices are positively related with the real interest rate.


Introduction
In terms of the background to this study (Note 1), whilst the area of research is financial economics, the aim is to benefit wealth management including Islamic wealth management.The wealth management industry is global in nature and asset allocation is strongly influenced by the behaviour of the USD, as the international reserve currency, in its relation to other currencies such as the Malaysian ringgit (RM).Hence, the research has a strong impact upon the Malaysian domestic wealth management industry in terms of portfolio allocation and re-balancing.Ahmad Husni Hanadzlah, Minister of Finance II, Malaysia, at the official launch of Labuan IBFC Wealth Management Year 2013, stated that "The wealth management industry is one of the fastest, if not THE fastest growing financial services sector in Malaysia and Southeast Asia.It is estimated that the number of our domestic high net worth individuals will double from its current 32,000 to 68,000 persons in 2015; with their net worth increasing in tandem from USD140 billion to USD330 billion (Bank Julius Baer, Switzerland, Asia Wealth Report, 2011)" (LIBFC).The research is essentially a quantitative study involving a systematic investigation of empirical evidence and statistics to develop a model price of gold that may be measured against the actual price to assess the accuracy of the forecasting performance.Qualitative interpretation of the empirical evidence is also required in order to analyze the causal significance between gold, interest rates and prices.
The current problem is that even though paper trades derive their price discovery from underlying physical trades, derivatives are clearly not simple hedging mechanisms, but in reality are highly speculative and even deemed potentially dangerous, when considered in aggregate.Warren Buffet stated in the Berkshire Hathaway annual report of 2002, that "derivatives are financial weapons of mass destruction" (Berkshire, 2002, p. 15).As at the end of 2013, the top five (5) U.S. banks have a combined notional value of derivatives of USD225.2Tn (OCC), which is 13.4 times U.S. GDP of USD16.8Tn, or 3 times global GDP of USD74.9Tn (World Bank).Specifically, J.P. Morgan has an alarming derivatives-to-risk-based capital ratio of 424:1, and Goldman Sachs' ratio has an astonishing 2,406:1.Banks such as J.P Morgan are heavily trading in interest rate as well as gold derivatives.Moreover, some commercial banks are on the gold fixing panel and also the LIBOR panel, and thus set both the gold price and the interest rate.Notwithstanding the level of risk and moral hazard that exists, it seems that banks with inside information are prepared to accept trading risks, confident in the knowledge that the financial markets are operating in their favour, given that the extent of forward volatility in relation to gold and interest rates is known.
The significance of this research is that an accurate gold price model would obviously be of interest to wealth managers, investors, indeed all economic agents interested in the future direction of returns within capital and commodity markets.On the other hand, it would also reveal that financial markets are not behaving in a free and fair manner, but are being "rigged" in the interests of those banks that are engaged in the price-setting manipulation of the value of money (in terms of the rate of exchange between the USD and an oz of gold) and the value of debt (in terms of the rate of interest, being the price of the supply of, and demand for, loanable funds), which has an effect on prices (inflation).Accordingly, the justification for the research is that since domestic wealth managers allocate their assets according to capital market expectations, then commodities (gold), interest rates and inflation (real interest rates) are all variables taken into consideration in the research.The USD and the returns on USD denominated assets are benchmarks for wealth managers, and LIBOR is the leading global interest rate impacting U.S. yields and also KLIBOR (being the benchmark interest rate for Malaysia).Essentially, this research involves three primary objectives: (i) to investigate the relationship between real short-term interest rates and the price of gold (PG) in relation to the Gibson's Paradox, from 1971-2013;(ii) to assess whether an equilibrium rate exists at which little or no movement occurs in the price of gold and investigate the extent of gold volatility in relation to changes in real interest rates; (iii) to evaluate the accuracy of a forecasting model for the price of gold in relation to the actual nominal price of gold.This paper is organized into five sections.In the first section we have provided an introduction, which includes a background to the research, highlighting the relevant issues and detailing the significance of the research.The second section provides a review of literature.The third sections details the methodology, the fourth section provides a discussion and analysis of the findings, and the fifth section provides concluding remarks.

Literature Review
Figure 1.Yields on consols and prices in England, 1791-1935(Abdullah, 2013, p. 37) Essentially, our research finds it origins in the Gibson paradox, which involves the co-movement of interest rates and prices, initially observed by a financial journalist, A.H. Gibson (1923Gibson ( , 1926)), that has been referred to as a paradox (by Keynes, 1930, p. 198), for it seemed to contradict the prediction of classical monetary theory that the interest rate is independent of the price level, being the price of the supply of, and demand for, loanable funds, whilst the price level is determined by the money supply, as described by the quantity theory of money.Many economists have failed to provide a satisfactory explanation including Wicksell (1907), Keynes (1930), Sargent (1973), Macaulay (1938), Friedman (1976), Fisher (1930), Shiller and Siegel (1977), and Barsky and Summers (1988).Abdullah (2013) provided empirical evidence that "under the gold standard, with the value of gold being held constant…nominal prices expressed in pounds coincided with real prices expressed in gold (the correlation  -1914).With the gold price constant, interest rates were low and held within a narrow band of 2-5%.The Gibson paradox is observed in the co-movement of interest rates and prices.Under the gold standard, in the absence of devaluation, nominal interest rates are real rates of interest, as gold is acquired at the nominal rate, given the convertibility of the currency" (Abdullah, 2013, p. 37).
Accordingly, the paradox was, and continues to be, a function central banking, whether under the 19th century gold standard or a 20th century fiat standard.Under the 19th century gold standard, "monetary policy was anchored to convertible bank notes (redeemable in gold coins), where the discount rate was a tool to adjust the supply of bank money in accordance with the gold standard, whilst the fiat standard is floating and anchored to the volume of debt, with fiat money being debt organized into money, so that the supply of money via the supply of debt, is the tool by which the market interest rate is adjusted in accordance to a central bank interest rate target" (Abdullah, 2013, p. 37).
Figure 2. Real prices and real interest rates in the U. S., 1971S., -2009S., (Abdullah, 2013, p. 40) , p. 40) Hence, in either case, monetary authorities vary the value of money in relation to the cost of borrowing, such that real interest rates have a positive relationship with real prices and an inverse relationship with the purchasing power of gold or real gold (Abdullah, 2013, pp. 39-40), so that the gold price can be managed by varying real interest rates (Abdullah, 2013, p. 42).Indeed, this was confirmed by the former Federal Reserve Governor Wayne Angell, whom admitted that "the price of gold is pretty well determined by us…but the major impact on the price of gold is the opportunity cost of holding the U.S. dollar…we can hold the price of gold very easily; all we have to do is to cause the opportunity cost in terms of interest rates and US Treasury bills, to make it unprofitable to own gold" (FOMC, 1993, pp. 40-41).
"Despite the importance of gold in central bank reserves and its value to investors as a store of wealth and potential risk diversifier, there is relatively little academic literature that attempts to estimate the price determinants [of gold]" (Oxford Economics, 2012).Others studies that have endeavoured to explain the determinants of the price gold purely in terms of the supply and demand of physical gold production, or through differing combinations of macro-economic variables, including inflation and associated volatility, exchange rates, money supply and stock prices, whether using moving averages (Khan, 2013) or regression techniques (Kaufmann, 1989), have adopted variables and approaches that involve historical data to forecast future movements in the price of gold (Shafiee, 2010).Moreover, further studies have highlighted the role of gold as a long run hedge against inflation, short-run hedge against exchange rate movement and a diversifier of risk in investment portfolios (Levine & Wright, 2006;Ghosh et al., 2002;Capie et al., 2005;Ibrahim, 2010;Erb & Harvey, 2013).Notwithstanding their approaches, the explanatory variables adopted, as key drivers of the gold price, largely reflect the underlying symptoms, which in reality relate to changes in the price of gold as a function of real interest rates.Since the purchasing power of money (PPM), or real money, is the inverse of nominal prices (CPI) expressed in fiat money (PPM = 1/CPI), then the purchasing power of gold (PPG), or real gold, is the inverse of real prices expressed in gold (PPG = 1/CPIg).The empirical evidence of the inverse relationship between real gold and real interest rates, or a positive relationship between real prices and real interest rates, analyzed and presented by Abdullah (2013) is also echoed in the empirical findings of Summers (Barsky, 1988) and Abken (1980), affirmed with the admission of gold and interest rate manipulation from the Federal Reserve in July 1993 (FOMC, 1993, pp. 40-41).

Methodology
Our research involves a full population of monthly gold price, inflation and interest rate secondary data are derived from various sources including the U.S. Department of Labor, the Federal Reserve, the World Gold Council, the Office of Comptroller of Currency (OCC), The Bank of International Settlements (BIS) and the World Bank.The descriptive statistics of this data will be used to test the hypothesis that the price of gold and interest rates are manipulated, which may be modelled through sensitivity analysis by showing the impact of a change in the level of interest rates with a change in the value of gold and vice versa.Accordingly, the conceptual framework assumes that the price of gold is the dependent variable as a function of changes in the real interest rates as the explanatory or independent variable, such that the nominal price of gold (PG) and real gold are inversely related with real interest rates.
As detailed by Abdullah (2013), the purchasing power of gold (PPG) or real gold, is defined as the index for the price of gold (PG) adjusted by inflation, which in this case is the consumer price index (CPI), The inverse of real gold (PPG) is real consumer prices expressed in gold (CPIg), The usual definition of real rate of interest rates (r) involves the nominal yield or rate of interest from 3-month Treasury bills (i), less the inflation rate as reflected in the CPI (π), We may assume that the change in the price of gold will vary against the change in short term real interest rates, but there may be an equilibrium real interest rate at which level, generally, little or no variance in the PG occurs.
The following linear equation may be adopted as the basic model for our research: The rate of change in real interest rates is statistically defined in the form of an index of real interest rates (i), derived from published Federal Reserve and Bureau of Labor statistics.By discounting or adjusting the index of (3-month U.S. Treasury bill) real interest rates (i), with the equilibrium real interest rate (r), and inverting the result, we obtain (a), being the difference between real interest rates and the equilibrium real interest rate (r).By applying a (monthly) rate of change in (a) to a percentage change in the nominal price of gold, we obtain the (monthly) percentage rate of change in the nominal price of gold (b), from which we can determine the model price of gold E(Y 1 ).Additional statistical analysis involves determining the correlation coefficient for a full population of monthly gold and real interest rate data to measure the strength of dependence between the model price of gold and the actual nominal price of gold, in order to assess its forecasting accuracy.

Discussion and Analysis
In this section we will present the nominal price of gold, the inflation adjusted price of gold and highlight specific instances of gold price suppression and in relation to nominal and real interest rates that could only realistically arise from central bank intervention on the gold price through interest rate manipulation.We will also indicate our equilibrium real interest rate, with which to factor into our equation (4.0.).This might also vary given changes in monetary policy and interest rate targets set by central banks.In any case, it provides a starting point to apply sensitivity analysis to the change in the price of gold in relation to real interest rates.We will then also present our model price of gold derived from changes in real interest rates and measure the accuracy through correlation in relation to the actual nominal price of gold.
With regard to the nominal price of gold from 1970-2013, we notice in figure 3, that the historical high of USD 850/oz that occurred on 21 January during the Iran-Iraq War, was surpassed on 5 September 2011 when it

E(Y 1 )
= expected nominal price of gold (USD per oz); a = the difference between real interest rates and the equilibrium real interest rate (r); b = the (monthly) percentage rate of change in the nominal price of gold; Y t-1 = nominal price of gold in the preceding period (USD per oz).

Real Interest Rates (%) 0 1 Log Real Prices Real Int Rate Real Prices
, financial and capital markets are neither free nor fair, but in reality, are highly manipulated and rigged.For the financial or wealth planner that understands this, interest rate and inflation expectations take on new meaning in generating and preserving wealth.